An optimal equity-linked pure endowment contract: optimal stochastic control approach

This article explores pure-endowment contracts with investments that are simultaneously allocated in risk-free and risky financial markets. Employing the optimal stochastic control method and assuming that the jumps of the risky financial market follow either a finite or infinite activity Lévy process, and that the policyholder’s utility function is a Constant Relative Risk Aversion (CRRA) utility function, the article derives an optimal investment strategy and optimal policyholder consumption, with dependency on the mortality rate. Various mortality models and jump parameters are utilized to investigate the sensitivity of our findings. Finally, the article establishes the fair price of such contracts under different circumstances, showcasing practical applications through several examples.