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Stochastic Models in Life Insurance / by Michael Koller
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: EAA Series | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012Description: Online-Ressource (XI, 219p. 41 illus., 33 illus. in color, digital)ISBN:- 9783642284397
- 368/.01 23
- 519.2
- QA273.A1-274.9 QA274-274.9
- QA273.A1-274.9
- QA274-274.9
Contents:
Summary: 1. A general life insurance model -- 2. Stochastic processes -- 3. Interest rate -- 4. Cash flows and the mathematical reserve -- 5. Difference equations and differential equations -- 6. Examples and problems from applications -- 7. Hattendorff's Theorem -- 8. Unit-linked policies -- 9. Policies with stochastic interest rate -- 10. Technical analysis -- 11. Abstract valuation -- 12. Policyholder bonus mechanism -- A. Notes on stochastic integration -- B. Examples -- C. Mortality rates in Germany -- D. Mortality rates in Switzerland -- E. Java code for the calculation of the Markov model -- References -- Notation -- Index.Summary: The book provides a sound mathematical base for life insurance mathematics and applies the underlying concepts to concrete examples. Moreover the models presented make it possible to model life insurance policies by means of Markov chains. Two chapters covering ALM and abstract valuation concepts on the background of Solvency II complete this volume. Numerous examples and a parallel treatment of discrete and continuous approaches help the reader to implement the theory directly in practice.PPN: PPN: 1651398453Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
"" Stochastic Modelsin Life Insurance""; ""Preface""; ""Contents""; ""1 A General Life Insurance Model""; ""1.1 Introduction""; ""1.2 Examples""; ""1.2.1 Types of Life Insurance""; ""1.2.2 Methods of Financing""; ""1.3 The Insurance Model""; ""2 Stochastic Processes""; ""2.1 Definitions""; ""2.2 Markov Chains on a Countable State Space""; ""2.3 Markov Chains in Continuous Time and Kolmogorov's Differential Equations""; ""2.4 Examples""; ""3 Interest Rate""; ""3.1 Introduction""; ""3.2 Definitions""; ""3.3 Models for the Interest Rate Process""; ""3.4 Stochastic Interest Rate""
""3.4.1 Discrete Time Interest Rate Models""""3.4.2 Continuous Time Interest Rate Models""; ""4 Cash Flows and the Mathematical Reserve""; ""4.1 Introduction""; ""4.2 Examples""; ""4.3 Fundamentals""; ""4.4 Deterministic Cash Flows""; ""4.5 Stochastic Cash Flows""; ""4.6 Mathematical Reserve""; ""4.7 Recursion Formulas for the Mathematical Reserves""; ""4.8 Calculation of the Premiums""; ""5 Difference Equations and Differential Equations""; ""5.1 Introduction""; ""5.2 Thiele's Differential Equations""; ""5.3 Examples: Thiele's Differential Equation""
""5.4 Differential Equations for Moments of Higher Order""""5.5 The Distribution of the Mathematical Reserve""; ""6 Examples and Problems From Applications""; ""6.1 Introduction""; ""6.2 Monthly and Quarterly Payments""; ""6.3 Pensions with Guaranteed Payment Periods""; ""6.4 Refund Guarantee""; ""6.5 Insurances with Stochastic Interest Rate""; ""6.6 Disability Insurance""; ""7 Hattendorff's Theorem""; ""7.1 Introduction""; ""7.2 Hattendorff's Theorem: General Setting""; ""7.3 Hattendorff's Theorem: Markov Model""; ""8 Unit-Linked Policies ""; ""8.1 Introduction""; ""8.2 Pricing Theory""
""8.2.1 Definitions""""8.2.2 Arbitrage""; ""8.2.3 Continuous Time Models""; ""8.3 The Economic Model""; ""8.4 Calculation of Single Premiums""; ""8.4.1 Pure Endowment Policy""; ""8.4.2 Term Life Insurance""; ""8.5 Thiele's Differential Equation""; ""9 Policies with Stochastic Interest Rate""; ""9.1 Introduction""; ""9.2 The Vasicek Model""; ""9.3 Value of the Portfolio""; ""9.4 A Model for the Interest Rate Structure""; ""9.5 Thiele's Differential Equation""; ""10 Technical Analysis""; ""10.1 Classical Technical Analysis""; ""10.2 Profit Testing""; ""10.3 Embedded Value""
""10.3.1 State Space""""10.3.2 Discount Function ""; ""10.3.3 Definition of the Policy Functions""; ""10.3.4 Examples""; ""11 Abstract Valuation""; ""11.1 Framework: Valuation Portfolios""; ""11.2 Cost of Capital""; ""11.3 Inclusion in the Markov Model""; ""11.4 Asset Liability Management""; ""12 Policyholder Bonus Mechanism""; ""12.1 Concept of Surplus: Traditional Approach and Legal Quote""; ""12.2 Portfolio Calculations""; ""12.3 Portfolio Dynamics and ALM""; ""12.4 Variable Annuities (VA)""; ""12.4.1 Introduction""; ""12.4.2 Product Design""; ""Appendix A Notes on Stochastic Integration""
""A.1�Stochastic Processes and Martingales""
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