Indifference pricing of pure endowments via BSDEs under partial information

TL;DR

This paper develops a framework for pricing pure endowment contracts under partial information using BSDEs, accounting for market incompleteness and mutual dependence between financial and insurance markets.

Contribution

It introduces a novel modeling approach combining filtering techniques with BSDEs to compute indifference prices under partial information.

Findings

Characterizes indifference prices via BSDE solutions.

Incorporates mutual dependence between financial and insurance markets.

Addresses market incompleteness due to basis risk.

Abstract

In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the so-called indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the indifference price of the insurance derivative via the solutions of suitable backward stochastic differential equations.