Merton's Portfolio Optimization with Multiple Risky Assets Based on Risk Preference
Abstract
This study addresses the issue of Merton portfolio optimization based on the Hyperbolic Absolute Risk Aversion (HARA) utility function within a finite time interval. The portfolio is constructed using two risky assets and one risk-free asset, ensuring that investments are not limited to a single risky asset in order to achieve optimal investment and consumption strategies. The mathematical model of the Merton portfolio problem will be analyzed using the Hamilton-Jacobi-Bellman (HJB) equation. The simulation shows that the optimal investment proportion in multi-risk assets decreases as wealth increases. This is influenced by the investor's risk preference relative to their wealth. The results also show that optimal consumption increases over time in order to obtain maximum utility.
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