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In this paper we investigate the pricing problem of a pure endowment contractwhen the insurer has a limited information on the mortality intensity of thepolicyholder. The payoff of this kind of policies depends on the residual lifetime of the insured as well as the trend of a portfolio traded in the financialmarket, where investments in a riskless asset, a risky asset and a longevitybond are allowed. We propose a modeling framework that takes into accountmutual dependence between the financial and the insurance markets via anobservable stochastic process, which affects the risky asset and the mortalityindex dynamics. Since the market is incomplete due to the presence of basisrisk, in alternative to arbitrage pricing we use expected utility maximizationunder exponential preferences as evaluation approach, which leads to theso-called indifference price. Under partial information this methodologyrequires filtering techniques that can reduce the original control problem toan equivalent problem in complete information. Using stochastic dynamicstechniques, we characterize the indifference price of the insurance derivativevia the solutions of suitable backward stochastic differential equations.

Indifference pricing of pure endowments via BSDEs under partial information