In this paper we investigate the hedging problem of a defaultable claim with recovery at default time via the local risk-minimization approach when investors have a restricted information on the market.  We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor and that at any time, investors may observe the risky asset price and know if default has occurred or not . We characterize the optimal  strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the defaultable claim with respect to the minimal martingale measure and the available information flow. Finally, 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  in a Markovian setting via filtering.
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.
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defaultable claim with recovery at default time
unit-linked life insurance contract
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when investors have
, when the insurer has
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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.
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and that at any time, investors may observe the risky asset price and know if default has occurred or not
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
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hedging
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defaultable
insurance
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Finally, we
We
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. Finally, we discuss applications