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Homotopy Analysis Method for Portfolio Optimization Problem Under the 3/2 Model

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Abstract

This paper considers the Merton portfolio optimization problem for an investor that aims at maximizing the expected power utility of the terminal wealth and intermediate consumption. Applying the homotopy analysis method, an analytical solution for value function as well as optimal strategy under the 3/2 model is derived, respectively. Compared with the existing explicit solutions for Merton problem under the 3/2 model, the formulas provide certain parameters with less requirement since the homotopy analysis method does not depend on the existence of small parameters in the equation. Finally, numerical examples are examined with the approach, and the proposed solution provides more accurate approximation as the number of terms in infinite series increases.

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Correspondence to Zhaoli Jia.

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This paper was supported by the Nature Science Research Project of Anhui Province, China under Grant No. 1808085MA18 and General Program of the National Natural Science Foundation of China under Grant No. 72071068.

This paper was recommended for publication by Editor CAO Zhigang.

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Yang, S., Jia, Z., Wu, Q. et al. Homotopy Analysis Method for Portfolio Optimization Problem Under the 3/2 Model. J Syst Sci Complex 34, 1087–1101 (2021). https://doi.org/10.1007/s11424-021-9286-1

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  • DOI: https://doi.org/10.1007/s11424-021-9286-1

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