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No-Good-Deal, Local Mean-Variance and Ambiguity Risk Pricing and Hedging for an Insurance Payment Process

Published online by Cambridge University Press:  09 August 2013

Łukasz Delong*
Affiliation:
Institute of Econometrics, Division of Probabilistic Methods, Warsaw School of Economics, Al. Niepodleglosci 162, 02-554 Warsaw, Poland, Tel. and Fax: +48 22 564 86 17, E-Mail: [email protected]

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.

Type
Research Article
Copyright
Copyright © International Actuarial Association 2012

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