Pricing of Unit-linked Life Insurance Policies

TLDR

Unit‑linked life insurance policies expose insurers to financial risk because the future benefit value depends on a stochastic process. The study derives single premiums and risk‑minimizing trading strategies for unit‑linked policies using arbitrage pricing and martingale theory. A partial differential equation for the premium reserve’s market value is derived and compared to Thiele’s actuarial equation. The resulting PDE includes novel terms, and the principle of equivalence remains valid under a new risk‑adjusted probability measure.

Abstract

Abstract The key feature of unit-linked or equity-linked life insurance policies is the uncertain value of the future insurance benefit. By issuing unit-linked insurances that guarantees the policy-holder a minimum benefit, the insurance company is exposed to financial risk. The value of the insurance benefit is assumed to be a function of a particular stochastic process. We use the financial theory of arbitrage pricing and martingale theory to derive single premiums for different policies. We derive risk-minimizing trading strategies describing how the issuing company can reduce financial risk. We derive a partial differential equation for the market value of the premium reserve which we compare to Thiele's equation of the actuarial sciences. Our equation contains some new terms stemming from our economic model. The interpretation of the principle of equivalence may be revisited in this framework; the principle still holds but under a new risk adjusted probability measure, equivalent to—but different from—the originally given probability measure.