Financial Modeling, Actuarial Valuation and Solvency in Insurance

Transcription

1 Springer Finance Financial Modeling, Actuarial Valuation and Solvency in Insurance Bearbeitet von Michael Merz, Mario V. Wüthrich 1. Auflage Buch. xiv, 432 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 830 g Wirtschaft > Finanzsektor & Finanzdienstleistungen: Allgemeines > Versicherungswirtschaft Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents 1 Introduction Full Balance Sheet Approach SolvencyConsiderations FurtherModelingIssues Outline of This Book... 6 Part I Financial Valuation Principles 2 State Price Deflators and Stochastic Discounting Zero Coupon Bonds and Term Structure of Interest Rates Motivation for Discounting Spot Rates and Term Structure of Interest Rates EstimatingtheYieldCurve Basic Discrete Time Stochastic Model ValuationatTime Interpretation of State Price Deflators Valuation at Time t> EquivalentMartingaleMeasure Bank Account Numeraire MartingaleMeasureandtheFTAP MarketPriceofRisk Spot Rate Models General Gaussian Spot Rate Models One-Factor Gaussian Affine Term Structure Models Discrete Time One-Factor Vasicek Model Spot Rate Dynamics on a Yearly Grid Spot Rate Dynamics on a Monthly Grid Parameter Calibration in the One-Factor Vasicek Model Conditionally Heteroscedastic Spot Rate Models Auto-Regressive Moving Average (ARMA) Spot Rate Models AR(1) Spot Rate Model vii

3 viii Contents AR(p) Spot Rate Model General ARMA Spot Rate Models Parameter Calibration in ARMA Models Discrete Time Multifactor Vasicek Model Motivation for Multifactor Spot Rate Models Multifactor Vasicek Model (with Independent Factors) Parameter Estimation and the Kalman Filter One-Factor Gamma Spot Rate Model Gamma Affine Term Structure Model Parameter Calibration in the Gamma Spot Rate Model Discrete Time Black Karasinski Model Log-Normal Spot Rate Dynamics Parameter Calibration in the Black Karasinski Model ARMA Extended Black Karasinski Model Stochastic Forward Rate and Yield Curve Modeling General Discrete Time HJM Framework GaussianDiscreteTimeHJMFramework General Gaussian Discrete Time HJM Framework Two-Factor Gaussian HJM Model Nelson Siegel and Svensson HJM Framework YieldCurveModeling DerivationsfromtheForwardRateFramework Stochastic Yield Curve Modeling Appendix Proofs of Chap Pricing of Financial Assets PricingofCashFlows General Cash Flow Valuation in the Vasicek Model Defaultable Coupon Bonds Financial Market A Log-Normal Example in the Vasicek Model A First Asset-and-Liability Management Problem PricingofDerivativeInstruments Appendix Proofs of Chap Part II Actuarial Valuation and Solvency 6 Actuarial and Financial Modeling Financial Market and Financial Filtration Basic Actuarial Model Improved Actuarial Model Valuation Portfolio ConstructionoftheValuationPortfolio Financial Portfolios and Cash Flows ConstructionoftheVaPo...171

4 Contents ix Best-EstimateReserves Examples Examples in Life Insurance Example in Non-life Insurance ClaimsDevelopmentResultandALM ClaimsDevelopmentResult Hedgeable Filtration and ALM ExamplesRevisited ApproximateValuationPortfolio Protected Valuation Portfolio ConstructionoftheProtectedValuationPortfolio Market-ValueMargin Risk-AdjustedReserves Claims Development Result of Risk-Adjusted Reserves Fortuin Kasteleyn Ginibre (FKG) Inequality Examples in Life Insurance Example in Non-life Insurance Further Probability Distortion Examples NumericalExamples Non-life Insurance Run-Off Life Insurance Examples Solvency RiskMeasures Definition of (Conditional) Risk Measures ExamplesofRiskMeasures Solvency and Acceptability Definition of Solvency and Acceptability FreeCapitalandSolvencyTerminology Insolvency No Insurance Technical Risk Theoretical ALM Solution and Free Capital General Asset Allocations Limited Liability Option MargrabeOption Hedging Margrabe Options Inclusion of Insurance Technical Risk Insurance Technical and Financial Result Theoretical ALM Solution and Solvency General ALM Problem and Insurance Technical Risk Cost-of-Capital Loading and Dividend Payments Risk Spreading and Law of Large Numbers Limitations of the Vasicek Financial Model PortfolioOptimization Standard Deviation Based Risk Measure Estimation of the Covariance Matrix

5 x Contents 10 Selected Topics and Examples Extreme Value Distributions and Copulas Parameter Uncertainty Parameter Uncertainty for a Non-life Run-Off Modeling of Longevity Risk Cost-of-Capital Loading in Practice General Considerations Cost-of-Capital Loading Example Accounting Year Factors in Run-Off Triangles Model Assumptions PredictiveDistribution Premium Liability Modeling Modeling Attritional Claims ModelingLargeClaims Reinsurance RiskMeasurementandSolvencyModeling Insurance Liabilities Asset Portfolio and Premium Income Cost Process and Other Risk Factors Accounting Condition and Acceptability Solvency Toy Model in Action Concluding Remarks Part III Appendix 11 Auxiliary Considerations HelpfulResultswithGaussianDistributions Change of Numeraire Technique General Changes of Numeraire Forward Measures and European Options on ZCBs European Options with Log-Normal Asset Prices References Index...427