The Uncertain Mortality Intensity Framework: Pricing and Hedging Unit-Linked Life Insurance Contracts

32 Pages Posted: 14 Jul 2010 Last revised: 13 Jun 2011

See all articles by Jing Li

Jing Li

Institute for Finanancial Economics and Statistics

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Date Written: July 5, 2010

Abstract

We study the valuation and hedging of unit-linked life insurance contracts in a setting where mortality intensity is governed by a stochastic process. We focus on model risk arising from different specifications for the mortality intensity. To do so we assume that the mortality intensity is almost surely bounded under the statistical measure. Further, we restrict the equivalent martingale measures and apply the same bounds to the mortality intensity under these measures. For this setting we derive upper and lower price bounds for unit-linked life insurance contracts using stochastic control techniques. We also show that the induced hedging strategies indeed produce a dynamic superhedge and subhedge under the statistical measure in the limit when the number of contracts increases. This justifies the bounds for the mortality intensity under the pricing measures. We provide numerical examples investigating fixed-term, endowment insurance contracts and their combinations including various guarantee features. The pricing partial differential equation for the upper and lower price bounds is solved by finite difference methods. For our contracts and choice of parameters the pricing and hedging is fairly robust with respect to misspecification of the mortality intensity. The model risk resulting from the uncertain mortality intensity is of minor importance.

Keywords: unit-linked life insurance contracts, mortality model risk, price bounds, stochastic control

JEL Classification: G13, G22, C61

Suggested Citation

Li, Jing and Szimayer, Alexander, The Uncertain Mortality Intensity Framework: Pricing and Hedging Unit-Linked Life Insurance Contracts (July 5, 2010). Available at SSRN: https://ssrn.com/abstract=1639336 or http://dx.doi.org/10.2139/ssrn.1639336

Jing Li (Contact Author)

Institute for Finanancial Economics and Statistics ( email )

Adenauerallee 24-42
Bonn, D-53113
Germany
0049-228-736104 (Phone)

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

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