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Financial Modeling, Actuarial Valuation and Solvency in Insurance 2013 ed. [Kõva köide]

  • Formaat: Hardback, 432 pages, kõrgus x laius: 235x155 mm, kaal: 7922 g, XIV, 432 p., 1 Hardback
  • Sari: Springer Finance
  • Ilmumisaeg: 17-Apr-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642313914
  • ISBN-13: 9783642313912
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  • Formaat: Hardback, 432 pages, kõrgus x laius: 235x155 mm, kaal: 7922 g, XIV, 432 p., 1 Hardback
  • Sari: Springer Finance
  • Ilmumisaeg: 17-Apr-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642313914
  • ISBN-13: 9783642313912
Teised raamatud teemal:
Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments in this area in the financial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wüthrich combine ideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fully consistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options, dividend to shareholder questions, the role of re-insurance, etc.

This work embeds the solvency discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in the financial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a good background in probability theory and statistics, and should be familiar with popular distributions, stochastic processes, martingales, etc.

Arvustused

From the reviews:

The purpose of this book is to introduce sound risk measurement practices which form bases of good risk management policies and solvency regulation. I warmly recommend this book to graduate students and researchers in applied mathematics, financial mathematics, actuarial science, solvency and insurance. The models proposed are original and very up-to-date. The book could be an essential tool for people working with financial modeling, actuarial valuation, and solvency in insurance. (Rzvan Rducanu, Mathematical Reviews, December, 2013)

1 Introduction
1(10)
1.1 Full Balance Sheet Approach
3(1)
1.2 Solvency Considerations
4(1)
1.3 Further Modeling Issues
5(1)
1.4 Outline of This Book
6(5)
Part I Financial Valuation Principles
2 State Price Deflators and Stochastic Discounting
11(24)
2.1 Zero Coupon Bonds and Term Structure of Interest Rates
11(7)
2.1.1 Motivation for Discounting
11(1)
2.1.2 Spot Rates and Term Structure of Interest Rates
12(3)
2.1.3 Estimating the Yield Curve
15(3)
2.2 Basic Discrete Time Stochastic Model
18(8)
2.2.1 Valuation at Time 0
19(3)
2.2.2 Interpretation of State Price Deflators
22(1)
2.2.3 Valuation at Time t > 0
23(3)
2.3 Equivalent Martingale Measure
26(5)
2.3.1 Bank Account Numeraire
26(1)
2.3.2 Martingale Measure and the FTAP
27(4)
2.4 Market Price of Risk
31(4)
3 Spot Rate Models
35(62)
3.1 General Gaussian Spot Rate Models
35(3)
3.2 One-Factor Gaussian Affine Term Structure Models
38(3)
3.3 Discrete Time One-Factor Vasicek Model
41(15)
3.3.1 Spot Rate Dynamics on a Yearly Grid
42(3)
3.3.2 Spot Rate Dynamics on a Monthly Grid
45(2)
3.3.3 Parameter Calibration in the One-Factor Vasicek Model
47(9)
3.4 Conditionally Heteroscedastic Spot Rate Models
56(4)
3.5 Auto-Regressive Moving Average (ARMA) Spot Rate Models
60(5)
3.5.1 AR(1) Spot Rate Model
61(1)
3.5.2 AR(p) Spot Rate Model
62(1)
3.5.3 General ARMA Spot Rate Models
63(1)
3.5.4 Parameter Calibration in ARMA Models
64(1)
3.6 Discrete Time Multifactor Vasicek Model
65(22)
3.6.1 Motivation for Multifactor Spot Rate Models
65(2)
3.6.2 Multifactor Vasicek Model (with Independent Factors)
67(5)
3.6.3 Parameter Estimation and the Kalman Filter
72(15)
3.7 One-Factor Gamma Spot Rate Model
87(5)
3.7.1 Gamma Affine Term Structure Model
87(3)
3.7.2 Parameter Calibration in the Gamma Spot Rate Model
90(2)
3.8 Discrete Time Black-Karasinski Model
92(5)
3.8.1 Log-Normal Spot Rate Dynamics
92(1)
3.8.2 Parameter Calibration in the Black-Karasinski Model
93(2)
3.8.3 ARMA Extended Black-Karasinski Model
95(2)
4 Stochastic Forward Rate and Yield Curve Modeling
97(34)
4.1 General Discrete Time HJM Framework
98(2)
4.2 Gaussian Discrete Time HJM Framework
100(6)
4.2.1 General Gaussian Discrete Time HJM Framework
100(2)
4.2.2 Two-Factor Gaussian HJM Model
102(3)
4.2.3 Nelson-Siegel and Svensson HJM Framework
105(1)
4.3 Yield Curve Modeling
106(19)
4.3.1 Derivations from the Forward Rate Framework
106(3)
4.3.2 Stochastic Yield Curve Modeling
109(16)
Appendix Proofs of Chap. 4
125(6)
5 Pricing of Financial Assets
131(24)
5.1 Pricing of Cash Flows
132(5)
5.1.1 General Cash Flow Valuation in the Vasicek Model
132(3)
5.1.2 Defaultable Coupon Bonds
135(2)
5.2 Financial Market
137(9)
5.2.1 A Log-Normal Example in the Vasicek Model
139(4)
5.2.2 A First Asset-and-Liability Management Problem
143(3)
5.3 Pricing of Derivative Instruments
146(3)
Appendix Proofs of Chap. 5
149(6)
Part II Actuarial Valuation and Solvency
6 Actuarial and Financial Modeling
155(14)
6.1 Financial Market and Financial Filtration
155(2)
6.2 Basic Actuarial Model
157(7)
6.3 Improved Actuarial Model
164(5)
7 Valuation Portfolio
169(36)
7.1 Construction of the Valuation Portfolio
170(7)
7.1.1 Financial Portfolios and Cash Flows
171(1)
7.1.2 Construction of the VaPo
171(3)
7.1.3 Best-Estimate Reserves
174(3)
7.2 Examples
177(10)
7.2.1 Examples in Life Insurance
177(4)
7.2.2 Example in Non-life Insurance
181(6)
7.3 Claims Development Result and ALM
187(10)
7.3.1 Claims Development Result
187(1)
7.3.2 Hedgeable Filtration and ALM
188(4)
7.3.3 Examples Revisited
192(5)
7.4 Approximate Valuation Portfolio
197(8)
8 Protected Valuation Portfolio
205(56)
8.1 Construction of the Protected Valuation Portfolio
205(2)
8.2 Market-Value Margin
207(27)
8.2.1 Risk-Adjusted Reserves
207(2)
8.2.2 Claims Development Result of Risk-Adjusted Reserves
209(2)
8.2.3 Fortuin-Kasteleyn-Ginibre (FKG) Inequality
211(2)
8.2.4 Examples in Life Insurance
213(10)
8.2.5 Example in Non-life Insurance
223(7)
8.2.6 Further Probability Distortion Examples
230(4)
8.3 Numerical Examples
234(27)
8.3.1 Non-life Insurance Run-Off
234(10)
8.3.2 Life Insurance Examples
244(17)
9 Solvency
261(76)
9.1 Risk Measures
261(7)
9.1.1 Definition of (Conditional) Risk Measures
261(4)
9.1.2 Examples of Risk Measures
265(3)
9.2 Solvency and Acceptability
268(10)
9.2.1 Definition of Solvency and Acceptability
268(6)
9.2.2 Free Capital and Solvency Terminology
274(3)
9.2.3 Insolvency
277(1)
9.3 No Insurance Technical Risk
278(21)
9.3.1 Theoretical ALM Solution and Free Capital
278(5)
9.3.2 General Asset Allocations
283(3)
9.3.3 Limited Liability Option
286(5)
9.3.4 Margrabe Option
291(5)
9.3.5 Hedging Margrabe Options
296(3)
9.4 Inclusion of Insurance Technical Risk
299(27)
9.4.1 Insurance Technical and Financial Result
300(2)
9.4.2 Theoretical ALM Solution and Solvency
302(7)
9.4.3 General ALM Problem and Insurance Technical Risk
309(4)
9.4.4 Cost-of-Capital Loading and Dividend Payments
313(8)
9.4.5 Risk Spreading and Law of Large Numbers
321(4)
9.4.6 Limitations of the Vasicek Financial Model
325(1)
9.5 Portfolio Optimization
326(11)
9.5.1 Standard Deviation Based Risk Measure
327(6)
9.5.2 Estimation of the Covariance Matrix
333(4)
10 Selected Topics and Examples
337(70)
10.1 Extreme Value Distributions and Copulas
337(2)
10.2 Parameter Uncertainty
339(17)
10.2.1 Parameter Uncertainty for a Non-life Run-Off
339(13)
10.2.2 Modeling of Longevity Risk
352(4)
10.3 Cost-of-Capital Loading in Practice
356(10)
10.3.1 General Considerations
356(2)
10.3.2 Cost-of-Capital Loading Example
358(8)
10.4 Accounting Year Factors in Run-Off Triangles
366(3)
10.4.1 Model Assumptions
366(2)
10.4.2 Predictive Distribution
368(1)
10.5 Premium Liability Modeling
369(12)
10.5.1 Modeling Attritional Claims
371(4)
10.5.2 Modeling Large Claims
375(1)
10.5.3 Reinsurance
376(5)
10.6 Risk Measurement and Solvency Modeling
381(21)
10.6.1 Insurance Liabilities
381(4)
10.6.2 Asset Portfolio and Premium Income
385(2)
10.6.3 Cost Process and Other Risk Factors
387(1)
10.6.4 Accounting Condition and Acceptability
388(2)
10.6.5 Solvency Toy Model in Action
390(12)
10.7 Concluding Remarks
402(5)
Part III Appendix
11 Auxiliary Considerations
407(12)
11.1 Helpful Results with Gaussian Distributions
407(1)
11.2 Change of Numeraire Technique
408(11)
11.2.1 General Changes of Numeraire
408(2)
11.2.2 Forward Measures and European Options on ZCBs
410(5)
11.2.3 European Options with Log-Normal Asset Prices
415(4)
References 419(8)
Index 427