In this paper we investigate the hedging problem of a unit-linked lifeinsurance contract via the local risk-minimization approach, when the insurerhas a restricted information on the market. In particular, we consider anendowment insurance contract, that is a combination of a term insurance policyand a pure endowment, whose final value depends on the trend of a stock marketwhere the premia the policyholder pays are invested. We assume that the stockprice process dynamics depends on an exogenous unobservable stochastic factorthat also influences the mortality rate of the policyholder. To allow formutual dependence between the financial and the insurance markets, we use theprogressive enlargement of filtration approach. We characterize the optimalhedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabedecomposition of the insurance claim with respect to the minimal martingalemeasure and the available information flow. We provide an explicit formula bymeans of predictable projection of the corresponding hedging strategy underfull information with respect to the natural filtration of the risky assetprice and the minimal martingale measure. Finally, we discuss applications in aMarkovian setting via filtering.
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