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In this paper, we investigate the pricing problem of a pure endowment contract when the insurance company has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time of the insured as well as the trend of a portfolio traded in the financial market, where investments in a riskless asset, a risky asset and a longevity bond are allowed. We propose a modeling framework that takes into account mutual dependence between the financial and the insurance markets via an observable stochastic process, which affects the risky asset and the mortality index dynamics. Since the market is incomplete due to the presence of basis risk, in alternative to arbitrage pricing we use expected utility maximization under exponential preferences as evaluation approach, which leads to the so-called indifference price. Under partial information this methodology requires filtering techniques that can reduce the original control problem to an equivalent problem in complete information. Using stochastic dynamics techniques, we characterize the indifference price of the insurance derivative in terms of the solutions of two backward stochastic differential equations. Finally, we discuss two special cases where we get a more explicit representation of the indifference price process. [ABSTRACT FROM AUTHOR]

In a participating endowment contract, the special loss compensation and profit sharing mechanism leads to heterogeneous benchmarks to distinguish the gain and loss for the policyholder's and the insurance company's S-shaped utilities. Because of the intense competition among the insurance companies and the requirement of the regulators, the benefits of the policyholders should be considered. As such, choosing the weighted utility of the two counterparts as the optimization objective is a rational setting. This setting induces a non-HARA (hyperbolic absolute risk aversion) and non-concave objective utility whose exact concavity and convexity are unknown. The difficulties not only come from this highly non-concave optimization problem, but also exist in the implicit integration of the optimum when solving the expected utilities of the two counterparts. We originally design an identification method to establish two categories of concave envelopes to solve the optimization problem, and propose an innovative numerical integration by substitution technique to deal with the implicit integration problem. The numerical simulation results recognize the existence of Pareto improvement of the two counterparts, which shows that the utilities of the policyholder and the insurance company can be simultaneously improved by switching into the weighted objective and appropriately amending the contract. [ABSTRACT FROM AUTHOR]