Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization

TL;DR

This paper develops a local risk-minimization framework for hedging unit-linked life insurance contracts under partial information, where the mortality hazard rate is unobservable and only death counts are observed.

Contribution

It introduces explicit formulas for optimal hedging strategies using projections of the survival process and addresses the filtering problem in a Markovian setting.

Findings

Explicit formulas for hedging strategies are derived.

The approach handles unobservable mortality hazard rates.

Filtering techniques are applied to a Markovian model.

Abstract

In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of insured individuals but not the mortality hazard rate. We consider a financial market driven by a general semimartingale and we aim to hedge unit-linked life insurance contracts via the local risk-minimization approach under partial information. The F\"ollmer-Schweizer decomposition of the insurance claim and explicit formulas for the optimal strategy for pure endowment and term insurance contracts are provided in terms of the projection of the survival process on the information flow. Moreover, in a Markovian framework, we reduce to solve a filtering problem with point process observations.