Option Pricing with Given Risk Constraints and Its Application to Life Insurance Contracts

This paper presents a method for hedging in markets of two-factor diffusion and jump diffusion models under the restriction of a specified probability of success. In addition, a method for hedging with a given shortfall amount is developed. A maximal perfect hedging set is constructed for options involving the exchange of one asset for another. The developed method is applied to the pricing of equity-linked life insurance contracts, such as “pure endowments with a guarantee”. Traditional pricing approaches for hedging options often yield minimal returns for investors. By accepting a predefined level of risk, investors can achieve higher returns. In light of this, this paper proposes risk management strategies applicable to these hybrid financial and insurance products.