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

C. Achudume; O.O. Ugbebor; S.O. Edeki; S.E. Fadugba

doi:10.56201/ijcsmt.vol.12.no7.2026.pg122.132

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

C. Achudume, O.O. Ugbebor, S.O. Edeki,, S.E. Fadugba

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.

Keywords

Power utility function; risk aversion; Itô’s Lemma; dynamic programming; market sensitivity; optimal portfolio JEL Classification: G11G12C61D81 IJCSMT IJCSMT

References

Ashrafi, H., Aurelie, & Thiele, C. (2021). A study of robust portfolio optimization with European options using polyhedral uncertainty sets. Operations Research Perspectives, 8, 100178. Balter, G.A., Mahayni, A., &Schweizer, N. (2021). Time-consistency of optimal investment under smooth ambiguity. European Journal of Operational Research, 293, 643–657. Brandtner, M., &Rishau, R. (2020). Beyond expected utility: Subjective risk aversion and optimal portfolio choice under convex shortfall risk measures. European Journal of Operational Research, 285(3), 1114–1126. Chen, H., &Xiong, C. (2026). Adaptive asset allocation with hierarchical reinforcement learning: A multi-class investment strategy. In Technical Innovation in Financial Economics: Advanced Theory, Practice, and Policy (pp. 163–188). IGI Global Scientific Publishing. Chen, X., & Zhang, W. (2021). Dynamic portfolio choice and information trading with recursive utility. Journal of Economic Modelling, 98, 154–167. Chen, Y., Verma, S., Greenman, K. P., Yin, H., Wang, Z., Wang, L., ... & Wang, X. (2026). A unified active learning framework for photosensitizer design. Chemical Science, 17(2), 916–926. Edeki, S.O. (2017). Analytical study and generalisation of selected stock option valuation models. Covenant University Institutional Repository. Edeki, S.O., Akinlabi, G.O., Egara, F.O., &Nzeadibe, A.C. (2020). Time-fractional classical Black–Scholes option pricing model via He-separation of variable transformation method for exact solutions. Journal of Physics: Conference Series, 1564(1), 012029. George, S., Kate, J., & Frank, E. (2025). The future of AI-driven portfolio optimization in biopharmaceutical program management, 1–8. Matthias, A., &Fahrenwaldt. (2020). Expected utility approximation and portfolio optimisation. Insurance: Mathematics and Economics, 93, 301–314. Merton, R.C. (1995). Financial innovation and the management and regulation of financial institutions. Journal of Banking & Finance, 19(3–4). Nkeki, C.I. (2018a). Optimal investment risks and debt management with back up security in a financial crisis. Journal of Computational and Applied Mathematics, 338, 129–152. Nkeki, C.I. (2018b). Optimal pension fund management in a jump-diffusion environment: Theoretical and practical studies. Journal of Computational and Applied Mathematics, 330, 228–252. Olanrewaju, A.G., Ajayi, A.O., Pacheco, O.I., Dada, A.O., &Adeyinka, A.A. (2025). AI-driven adaptive asset allocation: A machine learning approach to dynamic portfolio optimization in volatile financial markets. International Journal of Research in Finance and Management, 8(1), 320–332. Poledna, S., Martinez-Jaramilo, S., Caccioli, F., &Thurner, S. (2021). Quantification of systemic risk from overlapping portfolios in the financial system. Journal of Financial Stability, 52, 100808. Yu, B.W.-T., &Hau, S.H. (2009). Objective comparisons of the optimal portfolios corresponding to different utility functions. European Journal of Operational Research, 119(2), 604– 610.

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

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