Optimal Portfolio Strategy for A Sensitive Investor in A Dynamic Financial Market

Abstract

This paper investigates optimal portfolio choice for a risk-averse investor who is operating in a financial market characterized by continuous time usage and with explicit attention being paid to the investor's sensitivity to market movements. The investor's preferences are described by a power utility function of constant relative risk aversion, which promotes economically interesting behavior over wealth levels. The market consists of a risk-free asset and many risky assets, evolving under stochastic differential equations. By allowing the investor to adjust portfolio positions according to the changes in the processes of risky assets, the model can extend traditional portfolio optimization frameworks. Aiming to self-assemble against dynamic programming and the Hamilton-Jacobi-Bellman equation, exploiting Itô's calculus, we got analytical representations of the optimal portfolio strategy and its expected terminal utility. The quantification of the explicit sensitivity effect parameter allowed the activation of market responsiveness to additional advantage. Numerical simulations, with Python, demonstrate the role of market signals on a market-responsive portfolio. Two- and three-dimensional numerical figure analyses also depict the behavior, in terms of the optimal investment decisions, of risk aversion, asset volatility, and sensitivity parameters.