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Volume 9, Issue 3, June 2020, Page: 55-63
Investor’s Optimal Strategy with and Without Transaction Cost Under Ornstein-Uhlenbeck and Constant Elasticity of Variance (CEV) Models Via Exponential Utility Maximization
Silas Abahia Ihedioha, Department of Mathematics, Plateau State University Bokkos, Jos, Plateau State, Nigeria
Nanle Tanko Danat, Department of Mathematics, Plateau State University Bokkos, Jos, Plateau State, Nigeria
Audu Buba, Department of Actuarial Science, University of Jos, Jos, Plateau State, Nigeria
Received: Jun. 5, 2020;       Accepted: Jun. 20, 2020;       Published: Jul. 4, 2020
DOI: 10.11648/j.pamj.20200903.12      View  70      Downloads  52
Abstract
In this work, we studied the optimal investment problem of an investor who had exponential utility preference and traded two assets; (1) a risky asset which price dynamics was governed by the Constant Elasticity of variance (CEV) model and (2) a risk-free asset which price system followed the Ornstein-Uhlenbeck model. We employed the maximum principle of dynamic programming to obtain the Hamilton-Jacobi-Bellman (H-J-B) equation on which the first principle and the elimination of variable dependency were applied to get the closed-form of the investor’s optimal strategies. Two scenarios where the Brownian motions correlated and where they did not correlate were investigated. Also considered were the cases of when transaction cost was involved and when transaction cost was not involved. This lead to six cases that among the results obtained was that the investor has an optimal investment strategy that requires more amount of money for investment when the Brownian motions do not correlate and there is transaction cost than when the Brownian motions correlate and there is no transaction.
Keywords
Investor, Optimal Strategy, Transaction Cost, Ornstein-Uhlenbeck Model, Constant of Elasticity of Variance (CEV) Model, Exponential Utility Maximization
To cite this article
Silas Abahia Ihedioha, Nanle Tanko Danat, Audu Buba, Investor’s Optimal Strategy with and Without Transaction Cost Under Ornstein-Uhlenbeck and Constant Elasticity of Variance (CEV) Models Via Exponential Utility Maximization, Pure and Applied Mathematics Journal. Vol. 9, No. 3, 2020, pp. 55-63. doi: 10.11648/j.pamj.20200903.12
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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