Qualitative Analysis of Optimal Investment Strategies in Log-Normal Markets.

Summary We provide a concise study of the qualitative behavior of the optimal investment feedback policies and optimal weights, and of the local (absolute and relative) risk tolerance/risk aversion functions in a log-normal market model. We examine their spatial and temporal monotonicity, and their spatial concavity. We also examine their robustness with respect to the investor's risk tolerance coefficient as well as their dependence on the market parameters. We establish new results and provide short alternative proofs to existing ones.