Cover -- Half title -- Published Titles -- Title -- Copyright -- Contents -- Preface -- Chapter 1 Basic notions and facts from stochastic analysis, mathematical finance and insurance -- 1.1 Stochastic analysis -- 1.2 Contemporary stochastic analysis -- 1.3 Mathematical nance and insurance -- Chapter 2 Quantile hedging of equity-linked life insurance contracts in the Black-Scholes model -- 2.1 Quantile hedging of contracts with deterministic guarantees -- 2.2 Quantile hedging of contracts with stochastic guarantees -- 2.3 Quantile portfolio management with multiple contracts with a numerical example -- Chapter 3 Valuation of equity-linked life insurance contracts via effcient hedging in the Black-Scholes model -- 3.1 E cient hedging and pricing formulas for contracts with correlated assets and guarantees -- 3.2 E cient hedging and pricing of contracts with perfectly correlated stocks and guarantees -- 3.3 Illustrative risk-management for the risk-taking insurer -- Chapter 4 Quantile hedging and risk management of contracts for diffusion and jump-diffusion models -- 4.1 Quantile pricing formulas for contracts with perfectly correlated stocks and guarantees: Di usion and jump-di usion settings -- 4.2 Quantile hedging and an exemplary risk-management scheme for equity-linked life insurance -- Chapter 5 CVaR-Hedging: Theory and applications -- 5.1 CVaR-hedging methodology and general theoretical facts -- 5.2 CVaR-hedging in the Black{Scholes model with applications to equity-linked life insurance -- 5.3 CVaR-hedging in the regime-switching telegraph market model -- Chapter 6 Defaultable securities and equity-linked life insurance con- tracts -- 6.1 Multiple defaults and defaultable claims in the Black{Scholes model