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Title: No-Good-Deal, Local Mean-Variance and Ambiguity Risk Pricing and Hedging for an Insurance Payment Process
Author(s): DELONG, Łukasz
Journal: ASTIN Bulletin
Volume: 42    Issue: 1   Date: 2012   
Pages: 203-232
DOI: 10.2143/AST.42.1.2160741

Abstract :
We study pricing and hedging for an insurance payment process. We investigate a Black-Scholes financial model with stochastic coefficients and a payment process with death, survival and annuity claims driven by a point process with a stochastic intensity. The dependence of the claims and the intensity on the financial market and on an additional background noise (correlated index, longevity risk) is allowed. We establish a general modeling framework for no-good-deal, local mean-variance and ambiguity risk pricing and hedging. We show that these three valuation approaches are equivalent under appropriate formulations. We characterize the price and the hedging strategy as a solution to a backward stochastic differential equation. The results could be applied to pricing and hedging of variable annuities, surrender options under an irrational lapse behavior and mortality derivatives.