Preface |
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ix | |
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1 Basic notions and facts from stochastic analysis, mathematical finance and insurance |
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1 | (22) |
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1 | (5) |
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1.2 Contemporary stochastic analysis |
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6 | (7) |
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1.3 Mathematical finance and insurance |
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13 | (10) |
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2 Quantile hedging of equity-linked life insurance contracts in the Black---Scholes model |
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23 | (30) |
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2.1 Quantile hedging of contracts with deterministic guarantees |
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23 | (9) |
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2.2 Quantile hedging of contracts with stochastic guarantees |
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32 | (14) |
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2.3 Quantile portfolio management with multiple contracts with a numerical example |
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46 | (7) |
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3 Valuation of equity-linked life insurance contracts via efficient hedging in the Black---Scholes model |
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53 | (24) |
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3.1 Efficient hedging and pricing formulas for contracts with correlated assets and guarantees |
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53 | (11) |
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3.2 Efficient hedging and pricing of contracts with perfectly correlated stocks and guarantees |
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64 | (8) |
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3.3 Illustrative risk-management for the risk-taking insurer |
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72 | (5) |
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4 Quantile hedging and risk management of contracts for diffusion and jump-diffusion models |
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77 | (30) |
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4.1 Quantile pricing formulas for contracts with perfectly correlated stocks and guarantees: Diffusion and jump-diffusion settings |
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77 | (13) |
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4.2 Quantile hedging and an exemplary risk-management scheme for equity-linked life insurance |
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90 | (17) |
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5 CVaR-Hedging: Theory and applications |
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107 | (30) |
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5.1 CVaR-hedging methodology and general theoretical facts |
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107 | (8) |
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5.2 CVaR-hedging in the Black---Scholes model with applications to equity-linked life insurance |
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115 | (10) |
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5.3 CVaR-hedging in the regime-switching telegraph market model |
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125 | (12) |
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6 Defaultable securities and equity-linked life insurance contracts |
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137 | (26) |
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6.1 Multiple defaults and defaultable claims in the Black---Scholes model |
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137 | (6) |
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6.2 Efficient hedging in defaultable market: Essence of the technique and main results |
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143 | (15) |
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6.3 Application to equity-linked life insurance contracts: Brennan-Schwartz approach vs. the superhedging |
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158 | (5) |
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7 Equity-linked life insurance contracts and Bermudan options |
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163 | (24) |
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7.1 GMDB life insurance contracts as Bermudan options |
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163 | (7) |
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7.2 Quantile hedging of GMDB life insurance contracts |
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170 | (11) |
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7.3 Numerical illustrations |
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181 | (6) |
Bibliographic Remarks |
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187 | (6) |
Bibliography |
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193 | (6) |
Index |
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199 | |