of Complex Systems to ERM and Actuarial Work

Developments in the Application of Complex Systems to ERM and Actuarial Work Joshua Corrigan, Milliman Milliman

Agenda Overview of Complex Systems Sciences Strategic Risk Application and Example Operational Risk Application and Example Emerging Risk Applications and Example

A History of Complexity Science en.wikipedia.org/wiki/complexity_science

Actuarial Research 1. Concept Mapping (Networks) 2. Bayesian Networks 3. Phylogenetics 1. Networks 2. Cellular Automata 3. Artificial Societies 4. Serious Games

What is Systems Thinking? Worldview that: Process or methodology to: Problems cannot be addressed Understand complex system by a reduction of the system behaviour System behaviour is about See both the forest and the interactions and relationships trees Emergent behaviour is a result Identify possible solutions and of those interactions system learning Utilise complexity science techniques for risk analysis

Understanding Uncertainty Symptoms Causes Sense-making Understanding

A Company is a Complex Adaptive System Has a purpose p Emergence the whole has properties not held by sub components Self Organisation structure and hierarchy but few leverage points Interacting feedback loops causing highly non-linear behaviour Counter-intuitive and non-intended consequences Has tipping point or critical complexity limit before collapse Evolves and history is important Cause and symptom separated in time and space Risk is the unintended emergent property of a company

Agenda Overview of Complex Systems Sciences Strategic Risk Application and Example Operational Risk Application and Example Emerging Risk Applications and Example

Concept Mapping It s all in your head! People form complex models in their head of what they see/think. It is possible to use cognitive mapping techniques to reconstruct the highly complex risk profiles in a robust, repeatable way. You can evidence areas where narrative is too brief or where there are conflicting views. Source: Milliman It is a natural way for experts to engage but helps them combine their thoughts with others and identify the really important facts. Key Nodes Key Drivers Gaps

VA Business Case Study Source: Milliman

Business Drivers 76 Drivers 140 relationships Source: Milliman

What are the Key Drivers? Top 12 concepts / business drivers # immediate links Weighted links Cost of op risks 13 30 Product design and features 12 24 Operational hedge program 11 27 Appropriate hedge strategy 10 21 Cost of capital 10 31 Hedge effectiveness 8 26 Hedge costs for new business 7 23 Charges on new business 7 27 Liquidity and capital management 7 25 Distribution capability and effectiveness 6 10 Replication costs 6 24 Interest rates 5 28

What are the Critical Drivers and Most Potent Levers?

Identify Feedback Loops

Agenda Overview of Complex Systems Sciences Strategic Risk Application and Example Operational Risk Application and Example Emerging Risk Applications and Example

A Bayesian Approach Combine judgement and data Model built in terms of real business dynamics y More useful as a risk management tool Can simultaneously assess capital and non-capital outcomes Model can learn as observations are made Model can learn as observations are made Thank you to Rev Thomas Bayes ) ( ) / ( ) ( B B A B A P h ) ( ). / ( ) / ( ) ( ). / ( ), ( ) ( ). / ( ), ( A p A B p B A P A p A B p A B P B p B A p B A P where P(A) is the prior P(B/A)/P(B) is the evidence P(A/B) is the posterior ) ( ) / ( B p B A P P(A/B) is the posterior

Operational Risk Assessment

Monitoring Risk via Risk Indicators Source: Milliman

Translating Risk Appetite into Risk Limits Source: Milliman

Stress Test: Operating Under Constraints fds Source: Milliman

Agenda Overview of Complex Systems Sciences Strategic Risk Application and Example Operational Risk Application and Example Emerging Risk Applications and Example

Emerging Risk Risk registers typically force the assignment of a label to each entry (many one relationships) But the entries are often not that simple By using a more granular labeling approach it is still possible to aggregate the information o Technique from biology, phylogenetics or cladistics, permits analysis of: Which entries are like each other Understanding of how risk scenario characteristics evolve Clues about potential future scenarios

Cladistic approach Scenario Characteristics 1 2 3 4 5 6 A N N N N N N B Y Y N N N Y C Y N Y Y Y Y D Y N Y N Y N Most parsimonious solution (i.e. fewest changes)

Leverages Existing Information Builds on (enhanced) risk register info Extend range of characteristic ti classifiers

Evolutionary Risk Profile We can identify risks which share similarities, il iti common evolutionary paths and identify clues about future development Risks can be studied for a part of the company, or the whole

Emerging Risks BU 1 BU 3 BU 4 BU 2 BU 5 Tree shape Branches that have the most characters/adaptation Areas of bifurcation are likely areas for more evolution More likely to adapt again Find characters that evolve most frequently Is there a character or pattern that is responsible? Are any risks/branches losing characters, ask why? Any characters gained in sequence/coevolution Risks should generally increase in complexity Understand this pattern as a possible clue to new risks

Connectivity and Relationships Typical correlation measures cannot spot non-linear dependency. Mutual information sharing can Different levels of correlation Example Q ~ U[0,2p] R ~ U[4, 5] X = R cos Q Y = RsinQ Sample of 1000 Correlation = 0.0 Mutual Info = 1.0

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