Optimization of a time continuous portfolio of assets and derivatives

Rabieimotlagh, Omid

doi:10.22103/jmmr.2025.24238.1711

Optimization of a time continuous portfolio of assets and derivatives

Document Type : Research Paper

Author

Omid Rabieimotlagh

Department of Mathematics, University of Birjand, Birjand, Iran

10.22103/jmmr.2025.24238.1711

Abstract

‎We consider an incomplete market and suggest a self-financing time continuous investment strategy consisting of a risk-free asset (bond), a risky asset, and a financial derivative whose value moves inversely to that of the risky asset. We optimize the wealth process by introducing a parametric convex utility function that simultaneously maximizes wealth and minimizes the mean square of it. Using the HJB equation, we compute precisely the optimal portfolio process, where notably, a range of processes can optimize the problem. This advantage enables investors to gain fringe benefits while maintaining their overall investment strategy by adjusting their portfolios accordingly. As an application of the results, we optimize a portfolio process with a European put as the derivative and compute the corresponding optimal wealth numerically. Additionally, we will outline a method to calculate the market return rate and the martingale parameter, which are necessary for optimization.

Keywords

‎Self-finance portfolio

Dynamic programming

Wealth optimization

HJB equation

Subjects

Financial Mathematics

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