Unit-linked life insurance policies: optimal hedging in partially observable market models

TL;DR

This paper develops an optimal hedging strategy for unit-linked life insurance policies in markets with unobservable factors affecting stock prices and mortality, using advanced stochastic filtering and risk-minimization techniques.

Contribution

It introduces a novel approach to hedge insurance contracts under partial information by combining filtration enlargement, Galtchouk-Kunita-Watanabe decomposition, and explicit formulas in a Markovian setting.

Findings

Explicit hedging formulas derived under partial information.

Application of filtering techniques to estimate unobservable market factors.

Demonstration of the approach in a Markovian framework.

Abstract

In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering.