Optimal investment strategies for participating contracts

- Closed-form optimal investment strategies are established for managing participating contracts.
- Optimal strategies are derived under a utility maximization framework with an S-shaped utility function.
- A concavification technique and a pointwise optimization procedure are adopted with a martingale approach for the exploration of closed-form optimal solutions.
- A numerical procedure is applied for optimal solutions when investment strategies are constrained by an upper bound.

Participating contracts are popular insurance policies, in which the payoff to a policyholder is linked to the performance of a portfolio managed by the insurer. We consider the portfolio selection problem of an insurer that offers participating contracts and has an S-shaped utility function. Applying the martingale approach, closed-form solutions are obtained. The resulting optimal strategies are compared with portfolio insurance hedging strategies (CPPI and OBPI). We also study numerical solutions of the portfolio selection problem with constraints on the portfolio weights.