Risk-Minimizing Hedging Strategies for Unit-Linked Life Insurance Contracts

TLDR

Unit‑linked life insurance contracts tie benefits to the price of specific traded stocks, yet market incompleteness prevents full hedging with stocks and bonds alone, leaving insurers with residual risk. The authors model market uncertainty and the insured portfolio, apply risk‑minimization under a change of measure, and extend the framework to traded reinsurance contracts to eliminate risk entirely. They determine risk‑minimizing trading strategies and intrinsic risk processes for various unit‑linked contracts, and compute the corresponding self‑financing strategies.

Abstract

Abstract A unit-linked life insurance contract is a contract where the insurance benefits depend on the price of some specific traded stocks. We consider a model describing the uncertainty of the financial market and a portfolio of insured individuals simultaneously. Due to incompleteness the insurance claims cannot be hedged completely by trading stocks and bonds only, leaving some risk to the insurer. The theory of risk-minimization is briefly reviewed and applied after a change of measure. Risk-minimizing trading strategies and the associated intrinsic risk processes are determined for different types of unit-linked contracts. By extending the model to the situation where certain reinsurance contracts on the insured lives are traded, the direct insurer can eliminate the risk completely. The corresponding self-financing strategies are determined.