Before revision:  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 .
After revision:  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 .