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Dynamic mean-LPM portfolio optimization under the mean-reverting market

This paper studies the dynamic mean-LPM portfolio optimization problem with mean-reverting market. Rich empirical evidence shows that the stock return exhibits certain degree of mean-reverting property. However, the study of dynamic mean-risk model with mean-reverting market is rare in the literature. Due to the complicated constraints in this kind of dynamic optimization model, it is hard to use the stochastic control approach directly. Instead, under our market setting, we are able solve this problem semi-analyticall by using the martingale approach. Once the optimal terminal wealth is identified, we use some numerical approach and the Monte Carlo method to find the optimal wealth process and portfolio process for given state. Our method provide investor a simple tool to deal with the sophisticated model for guiding the portfolio management.