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Analysis Of Optimal Portfolio On Finite And Small-Time Horizons For A Stochastic Volatility Model With Multiple Correlated Assets

Author

Listed:
  • MINGLIAN LIN

    (Department of Mathematics, North Dakota State University, Fargo, ND 58105, USA)

  • INDRANIL SENGUPTA

    (Department of Mathematics and Statistics, City University of New York (CUNY)-Hunter College, New York, NY 10065, USA)

Abstract

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

Suggested Citation

  • Minglian Lin & Indranil Sengupta, 2024. "Analysis Of Optimal Portfolio On Finite And Small-Time Horizons For A Stochastic Volatility Model With Multiple Correlated Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 27(05n06), pages 1-32, September.
    • Handle: RePEc:wsi:ijtafx:v:27:y:2024:i:05n06:n:s0219024924500237
    DOI: 10.1142/S0219024924500237
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