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.
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