  In this paper we investigate the hedging problem of a unit-linked life
insurance contract via the local risk-minimization approach, when the insurer
has a restricted information on the market. In particular, we consider an
endowment insurance contract, that is a combination of a term insurance policy
and a pure endowment, whose final value depends on the trend of a stock market
where the premia the policyholder pays are invested. We assume that the stock
price process dynamics depends on an exogenous unobservable stochastic factor
that also influences the mortality rate of the policyholder. To allow for
mutual dependence between the financial and the insurance markets, we use the
progressive enlargement of filtration approach. We characterize the optimal
hedging strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe
decomposition of the insurance claim with respect to the minimal martingale
measure and the available information flow. We provide an explicit formula by
means of predictable projection of the corresponding hedging strategy under
full information with respect to the natural filtration of the risky asset
price and the minimal martingale measure. Finally, we discuss applications in a
Markovian setting via filtering.
