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Optimal Portfolio in a Regime-switching Model

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Book cover Seminar on Stochastic Analysis, Random Fields and Applications VII

Part of the book series: Progress in Probability ((PRPR,volume 67))

Abstract

In this paper we derive the solution of the classical Merton problem, i.e., maximizing the utility of the terminal wealth, in the case when the risky assets follow a diffusion model with switching coefficients. We show that the optimal portfolio is a generalisation of the corresponding one in the classical Merton case, with portfolio proportions which depend on the market regime. We perform our analysis via the classical approach with the Hamilton–Jacobi– Bellman equation. First we extend the mutual fund theorem as presented in [5] to our framework. Then we show explicit solutions for the optimal strategies in the particular cases of exponential, logarithm and power utility functions.

Mathematics Subject Classification (2010). 35K40, 60H30, 91G10, 91G80, 93E20.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of the Philippines – Diliman, Quezon City, Philippines, 1101

    Adrian Roy L. Valdez

  2. Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, I-35100, Padova, Italy

    Tiziano Vargiolu

Authors
  1. Adrian Roy L. Valdez
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  2. Tiziano Vargiolu
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Corresponding author

Correspondence to Adrian Roy L. Valdez .

Editor information

Editors and Affiliations

  1. Institut de Mathématiques (IMA) Chaire de Statistiques Appliquées (STAP), Ecole Polytechnique Fédérale de Lausanne Fac. Sciences de Base (FSB), Lausanne, Switzerland

    Robert C. Dalang

  2. Institut Elie Cartan, Université de Lorraine, Vandoeuvre-les-Nancy CX, France

    Marco Dozzi

  3. Unité de Mathématiques appliquées, ENSTA ParisTech, Palaiseau, France

    Francesco Russo

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Valdez, A.R.L., Vargiolu, T. (2013). Optimal Portfolio in a Regime-switching Model. In: Dalang, R., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications VII. Progress in Probability, vol 67. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0545-2_22

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