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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
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: lukasz.delong@sgh.waw.pl
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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.

Keywords

Hansen-Jagannathan boundinstantaneous Sharpe ratioequivalent martingale measureprobability priorsbackward stochastic differential equationvariable annuitieslongevity riskirrational lapse behavior
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 203 - 232
Copyright
Copyright © International Actuarial Association 2012

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