Risk Management of Extreme Events: The Role of Insurance and Protective Measures

Transcription

1 DRAFT COMMENTS WELCOMED Risk Management of Extreme Events: The Role of Insurance and Protective Measures Howard Kunreuther** Center for Risk Management and Decision Processes The Wharton School University of Pennsylvania Philadelphia, PA Visiting Research Scientist Columbia University Paper To Be Presented at First Paris International Conference on Risk and Insurance Economics Palais des Congres December 11, 2001

2 Risk Management of Extreme Events: The Role of Insurance and Protective Measures 1. Introduction A key question being raised since September 11 th is the appropriate role of the private and public sectors in reducing losses and offering insurance protection against extreme risks such as natural disasters, technological accidents and terrorist activities. The following two scenarios illustrate the challenges and opportunities facing the insurance and reinsurance industry in this regard: Scenario 1: Over the past 10 years the AllRisk (AR) Insurance Company has provided $ 500 million in coverage to Big Business (BB) Inc. against risks to its plant including terrorism. AR covers $100 million itself and has purchased an excess of loss reinsurance contract from Reinsurance Enterprise (RE) to cover the remaining $400 million. Given the events of Sept. 11 th RE has decided that terrorism will no longer be included in its coverage because of the uncertainties associated with the risk. BB needs terrorism coverage since the bank that holds its mortgage requires this as a condition for the loan. AR must decide whether or not to continue providing BB with the same type of insurance as it has had previously and if so how much coverage it is willing to offer. Scenario 2: The AR Insurance Company would like to encourage its clients to invest in fire prevention equipment such as sprinkler systems to reduce the potential losses from these risks. It has decided to offer a premium reduction for renters or homeowners coverage in any apartment unit that purchases a sprinkler system but needs to determine how large a discount it should give to them. Both these scenarios raise the following questions that this paper will address: 1. What factors determine whether the risk is insurable? 2. How much capital will AR require in order to provide protection against extreme events? 3. What role do externalities (i.e. losses caused by one party to other parties) play in setting premiums for insurance coverage? 4. What role can and should the public sector play in providing protection against extreme events? The next section addresses Question 1 by showing that uncertainty regarding the risks is likely to raise the premiums considerably particularly if one is concerned with the potential of large losses. Section 3 addresses Question 2 by focusing on the illustrative example depicted in Scenario 1 and showing that large amounts of capital are required to provide protection against uncertain events with large potential losses. In Section 4 I turn to Question 3 by focusing on Scenario 2 and showing that the premium reductions 2

3 which can be given to an individual investing in protective measures decreases if that person is contaminated by others who have not adopted these same measures. SThe paper then turns to Question 4 and contends that today there is a more important role for the public sector to play than ever before because of the uncertainties of the risks and the externalities associated with them. The paper concludes with a set of open questions for future research. 2. Insurability of Risks 1 What does it mean to say that a particular risk is insurable? This question must be addressed from the vantage point of the potential supplier of insurance who offers coverage against a specific risk at a stated premium. The policyholder is protected against a pre-specified set of losses defined in the contract. Two conditions must be met before insurance providers are willing to offer coverage against an uncertain event. Condition 1 is the ability to identify and quantify, or estimate, the chances of the event occurring, and the extent of losses likely to be incurred when providing different levels of coverage. Condition 2 is the ability to set premiums for each potential customer or class of customers. This requires some knowledge of the customer's risk in relation to others in the population of potential policyholders. If Conditions 1 and 2 are both satisfied, a risk is considered to be insurable. But it still may not be profitable. In other words, it may impossible to specify a rate for which there is sufficient demand and incoming revenue to cover the development, marketing and claims costs of the insurance and yield a net positive profit. In such cases the insurer will opt not to offer coverage against this risk. Condition 1: Identifying the Risk To satisfy this condition, estimates must be made of the frequency at which specific events occur and the extent of losses likely to be incurred. Such estimates can use data from previous events, or scientific analyses of what is likely to occur in the future. One way to reflect what experts know and do not know about a particular risk is to construct a loss exceedance probability (EP) curve. A loss EP curve depicts the probability that a certain level of loss will be exceeded on an annual basis. The loss can be reflected in terms of dollars of damage, fatalities, illness or some other measure. To illustrate with a specific example suppose one was interested in constructing an EP curve for dollar losses to structures in Paris from the flooding of the Seine. Using probabilistic risk assessment (PRA), one combines the set of events that could produce a given dollar loss and then determines the resulting probabilities of exceeding losses of different magnitudes. Based on these estimates, one can construct the mean EP depicted in Figure 1. By its nature, the EP curve inherently incorporates uncertainty in the probability of an event occurring and the magnitude of dollar losses. This uncertainty is reflected in the 5% and 95% confidence interval curves in Figure 1. 1 A more detailed discussion of insurability conditions can be found in Freeman and Kunreuther (1997). 3

4 Probability p(l) that losses will exceed L Uncertainty in Probability Uncertainty in Loss 95% Mean 5% Loss, L (in Dollars) Figure 2. Example of Exceedance Probability Curves The EP curve is the key element for evaluating a set of risk management tools. The accuracy of the EP curves depends upon the ability of the scientific and engineering community as well as social scientists to estimate the impact of events of different probabilities and magnitudes using the different units of analysis. These units normally include quantifiable measures such as dollar damage, number of people injured or killed and business interruption losses. When dealing with extreme events the key questions that need to be addressed when constructing an EP curve is the degree of uncertainty with respect to both the probability as well as the consequences of the event. It is a lot easier to construct an EP curve for natural disasters and chemical or nuclear power plant accidents than it is for terrorist activities. But even for these events there is considerable uncertainty with respect to both the probability of occurrence and the damage from these events. Here are a few questions in this regard that we may want to ponder: What are the chances that Paris will have severe flooding of the Seine next year and what will be the resulting damage and indirect losses? What is the likelihood of a severe nuclear power accident somewhere in France and what would be the resulting impacts? What are the chances that an airplane will crash into the business district in Paris in the next year and how serious would the consequences be? What are the chances that there will be a smallpox epidemic in Europe in the next five years and how many people would be affected? 4

5 Condition 2: Setting Premiums for Specific Risks Once the risk has been identified, the insurer needs to determine what premium it can charge to make a profit while not subjecting itself to an unacceptably high chance of a catastrophic loss. There are a number of factors that play a role in determining what prices companies would like to charge. In the discussion which follows we are assuming that insurers are free to set the premiums at any level they wish. In reality, state regulations often limit insurers in their rate-setting process. Ambiguity of Risk Not surprisingly, the higher the uncertainty regarding the probability of a specific loss and its magnitude, the higher the premium will be. As shown by a series of empirical studies, actuaries and underwriters are so averse to ambiguity and risk that they tend to charge much higher premiums than if the risk were well specified. Kunreuther, et al, (1995) conducted a survey of 896 underwriters in 190 randomly chosen insurance companies to determine what premiums would be required to insure a factory against property damage from a severe earthquake. The survey results examine changes in pricing strategy as function of the degree of uncertainty in either the probability and/or loss. A probability is considered to be well-specified where there is enough historical information on an event that all experts agreed that the probability of a loss is p. When there is wide disagreement about the estimate of p among the experts, this ambiguous probability is referred to as Ap. L represents a known loss that is, there is a general consensus about what the loss will be if a specific event occurs. When a loss is uncertain, and the experts estimates range between L min and L max, this uncertain loss is denoted as UL. Combining the degree of probability and loss uncertainty leads to four cases which are shown in the Table 1 along with a set of illustrative examples of the types of risks that fall in each category. INSERT TABLE 1 HERE To see how underwriters reacted to different situations, four scenarios were constructed as shown by the rows in Table 2.1. Where the risk is well-specified, the probability of the earthquake is either.01 or.005; the loss, should the event occur, is either $1 million or $10 million. The premium set by the underwriter is standardized at 1 for the non-ambiguous case; one can then examine how ambiguity affects pricing decisions. Table 2 shows the ratio of the other three cases relative to the non-ambiguous case (p, L) for the four different scenarios, which were distributed, randomly to underwriters in primary insurance companies. For the highly ambiguous case (Ap,UL), the premiums were between 1.43 to 1.77 times higher than if underwriters priced a non-ambiguous risk. The ratios for the other two cases were always above 1, but less than the (Ap,UL) case. 5

6 INSERT TABLE 2 HERE Adverse Selection If the insurer sets a premium based on the average probability of a loss, using the entire population as a basis for this estimate, those at the highest risk for a certain hazard will be the most likely to purchase coverage for that hazard. In an extreme case, the poor risks will be the only purchasers of coverage, and the insurer will lose money on each policy sold. This situation, referred to as adverse selection, occurs when the insurer cannot distinguish between the probability of a loss for good- and poor-risk categories. Moral Hazard Providing insurance protection to an individual may lead that person to behave more carelessly than before he or she had coverage. If the insurer cannot predict this behavior and relies on past loss data from uninsured individuals to estimate rates, the resulting premium is likely to be too low to cover losses. Moral hazard refers to an increase in the probability of loss caused by the behavior of the policyholder. Obviously, it is extremely difficult to monitor and control behavior once a person is insured. How do you monitor carelessness? Is it possible to determine if a person will decide to collect more on a policy than he or she deserves by making false claims? Correlated Risk Correlated risk refers to the simultaneous occurrence of many losses from a single event. As pointed out earlier natural disasters such as earthquakes, floods, and hurricanes produce highly correlated losses: many homes in the affected area are damaged and destroyed by a single event. If a risk-averse insurer faces a highly correlated losses from one event, it may want to set a high enough premium not only to cover its expected losses but also to protect itself against the possibility of experiencing catastrophic losses. An insurer will face this problem if it has many eggs in one basket, such as providing earthquake coverage mainly to homes in Los Angeles County rather than diversifying across the entire state of California. To illustrate the impact of correlated risks on the distribution of losses, assume that there are two policies sold against a risk where p =.1, L = $100. The actuarial loss for each policy is $10. If the losses are perfectly correlated, then there will be either two losses with probability of.1, or no losses with a probability of 9. On the other hand, if the losses are independent of each other, then the chance of two losses decreases to.01 (i.e.,.l x.1), with the probability of no losses being.81 (i.e.,.9 x.9). There is also a.18 chance that there will be only 1 loss (i.e.,.9 x x.9). 6

7 The expected loss for both the correlated and uncorrelated risks is $20. 2 However, the variance will always be higher for correlated than uncorrelated risks if each have the same expected loss. Thus, risk-averse insurers will always want to charge a higher premium for the correlated risk. Insurability Conditions and Demand for Coverage The above discussion suggests that in theory insurers can offer protection against any risk that they can identify, and for which they can obtain information to estimate the frequency and magnitude of potential losses as long as they have the freedom to set premiums at any level. However, due to problems of ambiguity, adverse selection, moral hazard, and highly correlated losses, they may want to charge premiums that considerably exceed the expected loss. For some risks the desired premium may be so high that there would be very little demand for coverage at that rate. In such cases, even though an insurer determines that a particular risk meets the two insurability conditions discussed above, it will not invest the time and money to develop the product. More specifically, the insurer must be convinced that there is sufficient demand to cover the development and marketing costs of the coverage through future premiums received. If there are regulatory restrictions that limit the price insurers can charge for certain types of coverage, then companies will not want to provide protection against these risks. In addition, if an insurer's portfolio leaves them vulnerable to the possibility of extremely large losses from a given disaster due to adverse selection, moral hazard, and/or high correlation of risks, then the insurer will want to reduce the number of policies in force for these hazards. 3. Capital Required by Insurers for Providing Protection One of the key issues that has been discussed recently is the amount of capital required by an insurer or reinsurer to provide protection against an extreme event. To address this question it is useful to focus on a concrete example such as the one in Scenario 1 that involves whether the AR Insurance Company can provide terrorism coverage to BB Inc. Situation Prior to September 11 th Recall from Scenario 1 that there was a potential loss to BB of $500 million with a probability equal to.01. Prior to September 11 th AR was able to obtain $ 400 million worth of reinsurance from RE so that it only had to cover $100 million of any losses that BB may have experienced. 2 For the correlated risk the expected loss is.9 x $0 +.1 x $200 = $20. For the independent risk the expected loss is (.81x$0) + (.18x$100) + (.01x$200) = $20. 7

8 Here is the relevant data on which RE based its premium to AR for reinsurance coverage: Loss to BB (L =$500) Probability of loss to BB (ρ=.01) Reinsurance coverage by RE to AR (L RE =$400 million) Expected Loss to RE (ρl RE =.01 (400)=4 million) RE loading factor (λ RE = 1) Reinsurance premium charged by RE to AR [Z RE = (1+ λ RE ) ρ L RE = 8] Assume that AR has a loading factor of λ AR =.5 so it charges BB a premium to cover the $500 million loss of Z AR = (1+ λ AR ) [ρ(l- L RE ) +Z RE ]. In other words AR charges BB a premium Z AR = [.01 (100) + 8 ](1.5) =13.5 for $500 million coverage and purchases $400 million worth reinsurance from RE. Situation After September 11 th Now that RE has decided to eliminate terrorist coverage in its reinsurance policies, AR has to determine how much protection it can offer BB Inc. and what price to charge for this coverage. The first concern of underwriters at AR is on the firm s safety and with profit maximization taking second place. 3 Stone (1973) formalized these concepts by suggesting that an underwriter will first focus on keeping the probability of insolvency below some threshold level (α): Pr (Loss >Premiums+Surplus) α For AR to offer BB $500 million in coverage, it now has to raise an additional $400 million in capital from different sources. One possibility would be for an investment bank to issue a $400 million cat bond to cover the losses from a terrorist attack. If investors are risk averse because of the uncertainty associated with the terrorist risk they will require a much larger than average return on their investment in order to cover the risk of losing their principal. Given the unusually high premiums on cat bonds for natural hazards risks where there is considerably less ambiguity and uncertainty than a terrorist attack this would not be surprising. 4 To illustrate, suppose investors require a 20% annual rate of return 5 for them to put money in a cat bond with the normal return on investments being 8%. In this case the 3 A safety-first model of firm behavior was first proposed by Roy (1952). Safety-first models explicitly concerns itself with insolvency when making a decision regarding maximum amount of coverage and premiums to charge. 4 For more detail on the high interest rates required by investors for cat bonds see Bantwal and Kunruether (2000). 5 The figure of 20% is based on recent discussions with insurers who are trying to raise capital for covering terrorist risks. 8

9 annual cost of AR obtaining $400 million through issuing a cat bond or from other sources of capital would be ( )$400 =.12 ($400) = $48 million = C For AR to offer BB insurance for next year given their additional costs of capital would be (pl AR + C) (1+ λ AR )= ($1 + 48) (1.5)= 73.5 which would be considerably more than BB would be willing to pay for $500 million worth of coverage. Under these conditions terrorist coverage is uninsurable. Note that even if investors only required a 12% return on the cat bond, AR would have to pay C= ( )($400) = $16 in which case its premium would be ($1+16)(1.5)=$25.5, which is still a very high price for BB Inc. to have to pay for property insurance. We will turn to the role of the public sector in providing protection against the terrorism risk in Section Rewarding Protection Against Extreme Risks: The Sprinkler Problem One of the ways that insurers can encourage its policyholders to invest in protective measures is to provide them with premium reductions to reflect the lower risk. For example, if a house has a sprinkler system then one would expect the premium for fire coverage to be reduced to reflect the lower risk. Unfortunately even unregulated insurers will not be able to provide premium incentives to encourage protection by a responsible party should there be other parties who do not adopt loss reduction measures against a similar event and contaminate the system. 6 When the number of irresponsible parties gets large there will be no economic incentive for any individual homeowner or firm to adopt protective measures that could be beneficial to them and to society. We will illustrate this point with a simple example one period example based on Scenario 2. A more detailed discussion with a more general result can be found in Heal and Kunreuther (2001). In Scenario 2 the AR Insurance Company wants to encourage apartment owners to invest in a sprinkler system to reduce the possibility of fire through a premium discount. 7 Suppose that the apartment building consists of two identical units: U 1 and U 2. The probability that U i will have a fire is p i and if it experiences a fire there is a probability q i that it will spread to the other unit. For ease of exposition assume that p 1 =p 2 = p and that q 1 =q 2 = q. Should a fire occur in unit i there is a loss of F i. Here again assume that the losses are the same in both units so that F 1 =F 2 =F. 6 Regulated insurers who are forced to charge premiums below their expected losses will have no incentive to reduce rates to reflect the reduced risk. They would normally prefer to cancel these insurance policies since they are losing money on them in the long run. 7 For simplicity but without loss of generality we are assuming that this is a one-period model. In reality protective investments provide benefits over many years. 9

10 If an apartment owner in U 1 invests in a sprinkler system at a cost of C then assume that the chances of a fire initiated in U 1 reduced to 0. If insurance premiums are based on risk, how much should they be reduced to reflect the expected reduction in losses from investing in a sprinkler system? If there were only one unit in the building then the answer would be pf, since it would be impossible for a fire to occur in this apartment. With an additional unit there is always the chance of a fire occurring in U 2 if it does not have a sprinkler system and then spreading to U 1. The AR Insurance Company thus can only determine what premium reduction it can offer U 1 by knowing whether or not U 2 has invested in a sprinkler system. This can be seen more clearly by constructing a simple 2x2 matrix reflecting the four possible conditions. Define S to be a decision to invest in a sprinkler system and N the decision not to invest in a sprinkler system. The expected costs associated with the fire risk are given in Table 3 with the first value in each box referring to the loss experience by U 1 and the second value referring to the loss experience by U 2 Let us look at each of the four boxes to understand how their values are constructed. If both units have a sprinkler system (S, S) then there is no loss from fire to either apartment and the total costs are simply the investment expenses for the sprinkler system (-C, C). On the other hand, if U 1 has invested in a sprinkler system while U 2 has not, then U 2 has a probability of experiencing a fire and causing losses of F (pf) and there is a chance that it will spread to U 1 and also cause losses of F (pqf). Thus even though U 1 will not have a fire in its own apartment, it may still be burned by unit 2 s flames. Hence the total costs associated with (S, N) is (-C pqf, -pf) as shown in the box in the upper right corner. The result is symmetrical if U 1 does not invest in a sprinkler system but U 2 does. (N, S), as shown in the lower left box of Table 3. Finally suppose that both units do not invest in a sprinkler system (N, N). Then the chances of a fire in each apartment is simply having a fire in one s own unit plus not having a fire in your unit and having one in the other unit that spreads to yours. [i.e. pf (1-p)pqF]. These are the costs shown for box (N, N) in the lower right hand box of Table 3. Table 3: Expected Costs Associated with Investing and Not Investing in Sprinklers UNIT 2 (U 2 ) UNIT 1 (U 1 ) S N S -C, -C -C -pqf, -pf N -pf, -C -pqf -pf - (1-p)pqF, -pf - (1-p)pqF The decision facing Units 1 and 2 as to whether or not to invest in a sprinkler system has the characteristics of a prisoner s dilemma problem. Consider the choice facing U 1. If U 2 has a sprinkler system (S) then the condition for U 1 to purchase one 10

11 is determined by looking at the difference between the costs of (S,S) and (N,S) which is simply C <pf. On the other hand, if U 2 does not have a sprinkler system (N) then U 1 will only want to invest in one if the costs of (S, N) is greater than the costs of (N,N). The condition for this to be true is that C< pf-p 2 qf. In other words, it is less likely that U 1 will want to adopt a protective measure if U 2 decides not to invest in one. The impact of contamination on the decision by AR on how much it should reduce its premium should now be clear. If Unit 2 does not have a sprinkler system then AR cannot reduce the premium that U 1 will have to pay by as much as pf because there is a chance that U 2 will have a fire and it will spread to Unit 1 In general, the more apartment units that do not invest in sprinkler systems the greater the chance that U 1 will suffer a loss from a fire even it has invested in its own sprinkler. Hence the lower the premium reduction that AR can give to the apartment owner for investing in protection. This point can be illustrated more clearly with a numerical example. Suppose that p=.1, q=.8, F=1000 and C= 95. The matrix in Table 3 is now represented as Table 4: Table 4: Expected Costs Associated with Investing and Not Investing in Sprinklers p=.1, q=.8, F=-1000 and C=95 UNIT 2 UNIT 1 S N S -95, , -100 N -100, , -172 One can see that if U 2 has a sprinkler system (S), then it is worthwhile for U 1 to also invest in one, since unit 1 s fire premiums will be reduced by pf= -100 and it will only have to spend 95 on the sprinkler. However, if U 2 does not invest in the sprinkler system (N), then there is still a chance that a fire will occur in U 1, so that the benefits of the sprinkler will be reduced and AR can only offer a premium reduction of 100-8=92. This is less than the 95 that the sprinkler system costs. 5. Role of Public and Private Sectors for Dealing with These Problems The analyses of these two scenarios raise a set of key questions as to what the roles of the public and private sectors should be in providing protection against extreme events. There are three issues that will be addressed in this section: What type of federal reinsurance protection would be appropriate for dealing with the terrorism risk? What is the experience of the UK in dealing with terrorism protection? 11

12 What role should the public sector play in encouraging protection against extreme events? Role of Federal Reinsurance If it is really true that investors are unwilling to provide capital to insurers or reinsurers for coverage against terrorism without obtaining a very high return as shown in Section 3, then there may be a need for some type of public sector involvement at least in the short-run. The U.S. Congress is now considering legislation to address this issue. There has also been testimony by researchers who indicate that some type of federal protection can be justified in the short-run but that the length of time for this form of protection should be limited. Ken Froot (2001) in his testimony makes the point that any federal intervention must encourage private market incentives to expand capacity as needed and diversify risk. It must generate appropriate price incentives to encourage the private sector to mitigate the losses and risk of a terrorist event. And it should help reduce uncertainty about liabilities that arise from associated litigation. Most importantly, I believe short sunset feature of the program is absolutely essential. Similarly David Cummins (2001) in his Congressional testimony indicates that the insurance industry has provided coverage for other uncertain events which lacked statistical reliability such as political risk insurance and satellite launches. It is likely that the private market can eventually develop pricing for terrorism coverage as it has for other uncertain and unique risks. Therefore any Federal involvement should be done in such a way as to not discourage private industry from returning to this market. A key question that needs to be addressed in developing some type of federal reinsurance program is who should pay for the costs while this system is in operation. If terrorism is viewed as a national problem with the costs borne by all taxpayers rather than just those who suffer losses, then some type of tax on all citizens might be appropriate. Alternatively all property owners who purchased insurance would have to pay a special terrorism surcharge to cover losses that have occurred. If on the other hand, Congress feels that the costs of terrorism should be borne by those who are at risk, then insurers who provide terrorism coverage should have to cover the cost of reinsurance. Suppose that the US Government set up a Terrorism Reinsurance Fund (TRF) to cover losses above a certain amount. Looking at Scenario 1, the AR Insurance Company would either have to pay TRF for reinsurance just as it was paying RE before Sept. 11 th. The actual premium it would have to pay would depend on estimates of the probability of future terrorist attacks (ρ) and the resulting claims that AR would have to pay (L). Instead if after a terrorist attack Congress created TRF to cover any losses above a certain amount through some type of loan arrangement, then insurers who required these funds would have to be the ones to repay them to TRF. 12

13 Experience of the UK with Terrorism Coverage It may be useful to study the experience that other countries have had with terrorism coverage. In the UK a mutual insurance organization (Pool Re) was established at the beginning of 1993 by the insurance community and the Government to accommodate claims following terrorist activities. The motivation for forming Pool Re came from two terrorist bomb explosions in the City of London in April 1992 and an announcement seven months later by British insurers that they would exclude terrorism coverage from their commercial policies (Fleming 1993). Pool Re charges a separate, optional premium for terrorism cover that is calculated as a percentage of the total fire and accident coverage. This premium is collected by the primary insurer and passed on to Pool Re. If a claim is made which exhausts the premiums collected, each primary insurer faces a levy of up to 10 percent of the premiums it has paid into the pool. If this amount cannot cover the cost of the claim then the balance is met out of the public purse. (CII Journal 1993). The premiums established by Pool Re are based on the risks with the highest rates in Central London and the second highest in the rest of the city. The lowest rates are in the rural parts of Scotland and Wales. Since this coverage is voluntary there were a number of businesses in the high risk areas of London who were uninsured because they felt the premiums were too high. (CII Journal 1993). Role of Government in Providing Protection Let me now turn to the question that has been preoccupying the United States in recent weeks: What is the appropriate role of the public and private sectors in providing protection against terrorism? Prior to September 11 th, there was certainly a concern with terrorism but there was also a feeling that it will not happen in my backyard. The private sector was expected to finance protective measures rather than relying on government for any assistance. Take the airline industry, for example. Before the World Trade Center and Pentagon attacks, if an airline wanted to invest in more secure cockpits or armed guards on the flight they would have had to incur these expenses themselves. Each company decided there was no incentive for it to take this action on its own, in part because they may not have felt the risks warranted such action but also because of competitive pressures. If one airline had invested in these protective measures, it would have incurred higher costs than the others. Furthermore there would have been little, if any, appreciation by the flying public as to why these measures were even necessary. Hence passengers would have been reluctant to pay higher ticket prices necessary to cover these additional expenses. In short, increased airline protection was a losing proposition for a single company. 13

14 The world has changed in the last twelve weeks. Government now feels it has to bail out the airline industry given that many companies are on the verge of bankruptcy. There is now recognition that an airplane can be used to kill many more people than just the passengers and crew, and create havoc by damaging property and causing large-scale business interruptions. This recognition and the resulting fear of flying by many people has created a demand for safer planes and increased security at airports. In the future much, if not all, of the costs of these protective measures is likely to be absorbed by the federal government. On a more general note, the terrorist attacks offer an opportunity to reassess the role of the public and private sector with respect to providing protection. One needs to recognize that for many situations there may be a need for the public sector to take the lead role as shown by the sprinkler example in Scenario 2. To illustrate this point, consider Airline A that is considering whether to institute a system to check their incoming bags, knowing that none of the other airlines have instituted such a system. Hence there is some chance that an unchecked bag from Airline B, C, D or E could be transferred to one of Airline A s planes. It turns out that if there is a relatively high chance that such an event will occur then there is no incentive for Airline A to undertake this protective measure under the current liability and insurance systems (Heal and Kunreuther 2001). It is thus not surprising that the US government has recently required that all baggage be checked by the airlines. 5. Conclusions and Open Issues This paper has addressed the question as to the appropriate role of the public and private sectors in reducing the likelihood and consequences of future extreme events through protective measures as well as providing insurance to cover losses should a disastrous event occur. There are a number of open questions that need to be addressed to deal with the problem of managing extreme events. The paper concludes by raising some of them as it applies to the terrorism problem: Can one develop meaningful scenarios to estimate the probability of future terrorist activities occurring (e.g. chances of a plane crashing into another building; chance of an individual contracting anthrax and recovering from the disease or dying from the disease)? Can one develop estimates of the losses from these events for which the insurer will be held responsible (e.g. property damage and business interruption from another terrorist attack; hospital expenses for individuals contracting anthrax)? 14

15 How much extra premiums will the insurer want to charge due to the ambiguity of the terrorist risk? Is there an adverse selection problem associated with terrorism? (i.e. only those in the high risk category want insurance and the insurer cannot distinguish between high and low risks?) Is there a moral hazard problem associated with terrorism? (i.e. those who buy insurance behave more carelessly than those who don t?) High likely is that losses from terrorist activities will be highly correlated? (e.g several planes crashing simultaneously; a smallpox epidemic) Will the premiums charged by insurers be affordable by those who are demanding terrorist coverage? What roles should the government and private sector play in providing protection against terrorism activities? There are no easy answers to these questions but they need to be addressed by insurers, reinsurers and the public sector to determine under what conditions private companies can provide coverage against terrorism and other extreme events. We also need to determine what roles the private sector and government should play in reducing the likelihood of these events occurring in the future and making them insurable risks. 15

16 SELECTED REFERENCES Bantwal, Vivek and Kunreuther, Howard (2000) A Cat Bond Premium Puzzle? Journal of Psychology and Financial Markets 1: CII Journal (1993) The Fate of Pool Re September pp Croson, D. C., and H. C. Kunreuther (2000). Customizing Indemnity Contracts and Indexed Cat Bonds for Natural Hazard Risks. Journal of Risk Finance, 1: Croson, D. and A. Richter (1999). Sovereign Cat Bonds and Infrastructure Project Financing. Working Paper , Wharton Risk Management and Decision Processes Center. University of Pennsylvania; Philadelphia, PA. Forthcoming, Risk Analysis. Cummins, David (2001) Protecting Policyholders from Terrorism: Private Sector Solutions Testimony before Subcommittee on Capital Markets, Insurance and Government Sponsored Enterprises US House of Representatives Oct. 24. Cummins, J. and Doherty, N. (1999). Can Insurers Pay for the Big One? Measuring the Capacity of an Insurance Market to Respond to Catastrophic Losses. Working Paper, The Wharton School, University of Pennsylvania. Cummins, J.D., D. Lalonde, and R. Phillips (1999). Basis Risk of Index-Linked CAT Risk Securities. Presented at June 14-15, 1999 meeting of Wharton Project on Managing Catastrophic Risks, Philadelphia, PA. Dionne, Georges and Harrington, Scott ed. (1992) Foundations of Insurance Economics (Kluwer: Boston). Dionne, Georges (ed) (1991) Contributions to Insurance Economics (Kluwer: Boston). Dionne, Georges (ed) (2001) Handbook of Insurance,, Boston: Kluwer Academic Publishers. Doherty, N. (1997). Financial innovation for financing and hedging catastrophe risk. in Financial Risk Management for Natural Catastrophes, edited by N.R. Britton, and J. Oliver, Brisbane: Doherty, N. and Richter, A. (2000). Moral Hazard, Basis Risk and Gap Insurance. Working Paper, Wharton Project on Managing Catastrophic Risks, November Dong, W., Shah, H., Wong, F. (1996). A Rational Approach to Pricing of Catastrophe Insurance Journal of Risk and Uncertainty, 12:

17 Earthquake Engineering Research Institute (1998). Incentives and Impediments in Improving the Seismic Performance of Buildings. Oakland, CA, EERI. Earthquake Engineering Research Institute (2000). Financial Management of Earthquake Risk. Oakland, CA: EERI Fleming, Alan (1993) The Role for Pool Re Proceedings of Property Owners Insurance Conference: Problems and Soloutions pp Freeman, Paul K, and Kunreuther, Howard (1997). Managing Environmental Risk Through Insurance (Boston: Kluwer; Washington, DC: American Enterprise Institute) Froot, Kenneth (2001) Testimony Before the US Senate Committee on Banking, Housing, and Urban Affairs. October 24.. Froot, K. (ed) (1999). The Financing of Property/Casualty Risks, Chicago: University of Chicago Press. Froot, Kenneth The Market for Catastrophe Risk: A Clinical Examination J of Financial Economics : Grace, M., R. W. Klein and P. R. Kleindorfer (2000). Supply and Demand of Catastrophe Insurance, Working Paper, Risk Management and Decision Processes Center, The Wharton School, Philadelphia, PA. Grossi, P. (2000). Quantifying the Uncertainty in Seismic Risk and Loss Estimation, Dissertation, Department of Systems Engineering, University of Pennsylvania. Heal, Geoffrey and Kunreuther, Howard (2001) Indeterdependent Security: The Role of the Weakest Links (in preparation) Insurance Services Office (1999). Financing Catastrophe Risk: Capital Market Solutions New York, N.Y.: Insurance Services Office. Kleindorfer, P. R. and Kunreuther, H. (1999). Challenges Facing the Insurance Industry in Managing Catastrophic Risks in Kenneth Froot (ed) The Financing of Property/Casualty Risks, Chicago: University of Chicago Press. Kleindorfer, P. R. and Kunreuther, H. (1999). The Complimentary Roles of Mitigation and Insurance In Managing Catastrophic Risks, Risk Analysis, 19: Kunreuther, H., J. Meszaros, R. Hogarth, and M. Spranca. (1995). Ambiguity and underwriter decision processes, Journal of Economic Behavior and Organization, 26:

18 Kunreuther, H. and Roth, R., Sr. ed. (1998). Paying the Price: The Status and Role of Insurance Against Natural Disasters in the United States. Washington, D.C: Joseph Henry Press. Lewis, Christopher, and Lewis Murdock. (1996). The role of government contracts in discretionary reinsurance markets for natural disasters. Journal of Risk and Insurance, 63: Mayers, D., and Smith, C. (1982). On corporate demand for insurance, Journal of Business, 55: Pauly, Mark (1974) Overinsurance and Public Provision of Insurance: The Role of Moral Hazard and Adverse Selection Quarterly Journal of Economics 88: Roy, A.D. (1952). Safety-First and the Holding of Assets, Econometrica, 20: Standard & Poors (2000). Sector Report: Securitization, June. Stone, J. (1973). A theory of capacity and the insurance of catastrophe risks: Part I and Part II, Journal of Risk and Insurance 40: (Part I) and 40: (Part II). Zeckhauser, Richard (1996) "The Economics of Catastrophes," Journal of Risk and Uncertainty, 12:

19 Table 1 Classification Of Risks By Degree Of Ambiguity And Uncertainty LOSS KNOWN UNKNOWN PROBABILITY WELL-SPECIFIED Case 1 p, L Life, auto, fire Case 3 p, UL Playground accidents AMBIGUOUS Case 2 Ap, L Satellite Case 4 Ap, UL Earthquake, Bioterrorism 19

20 Table 2 Ratios of Underwriters Actuarial Premiums for Ambiguous and/or Uncertain Earthquake Risks Relative to Well-Specified Risks CASES SCENARIO p,l Ap,L p,ul Ap,UL p=.005 L=$1 million pl=$5,000 p=.005 L=$10 million pl=$50,000 p=.01 L=$1 million pl=$10,000 p=.01 L=$10 million pl=$100,000 Source: Kunreuther et al