In this paper we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and another company , and the default of the company induces an immediate drop in the stock price of the surviving company . We prove  the value function is the unique continuous viscosity solution of the HJB equation. We also  compare and analyse the statistical distributions of  terminal wealth of log utility  based on two optimal strategies, one using the full information of intensity process , the other a proxy constant intensity process . These two strategies may be considered respectively the active and passive optimal portfolio investment. Our simulation results show that, statistically, active portfolio investment is more volatile and performs either much better or much worse than the passive portfolio investment in extreme scenarios .
In this paper we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies , and the default of the company induces immediate drops in the stock prices of the surviving companies . We prove that the value function is the unique viscosity solution of the HJB equation. We also perform some numerical tests to compare and analyse the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process .
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another company
other companies
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an immediate drop
immediate drops
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price
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company
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continuous
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perform some numerical tests to
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the
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and power utility
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optimal
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. These two strategies may be considered respectively the active and passive optimal portfolio investment. Our simulation results show that, statistically, active portfolio investment is more volatile and performs either much better or much worse than the passive portfolio investment in extreme scenarios