Design and management of unit-linked life-insurance contracts with guarantees

In this chapter, modeling and optimal management of unit-linked life insurance contracts with guarantee (ULLIG) is considered. The insurance premium inflow is invested to build a customer-specific portfolio. The minimal guarantee obliges the insurance company to pay either some pre-specified guaranteed sum or the actual accumulated portfolio value. Such contracts require a careful hedging against possible shortfalls. Both a discrete-time as well as a continuous-time version of this management problem is discussed. In the discrete-time case, the problem is formulated as a multi-stage stochastic optimization model. This specific modeling instance aims at maximizing expected portfolio value, and penalizes possible losses. Such classes of models can conveniently be utilized to assess shortfall risk and to optimally design new contracts. In the latter case, main parameters of the contract are determined, such that they meet the customers needs, and include constraints to meet regulatory as well as organizational constraints of the insurance company. Simulation studies can be applied to achieve an optimal contract design. The continuous-time modeling approach of optimal portfolio allocation in a guarantee setting with regular premium inflows and random benefit outflows provides further theoretical insights.