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Simulating Portfolio Decisions under Uncertainty When the Risky Asset and Short Rate Are Modulated by an Inhomogeneous and Asset-Dependent Markov Chain

Author

Listed:
  • Benjamín Vallejo-Jiménez

    (Facultad de Economía, Universidad de Colima, Colima 28970, Mexico)

  • Francisco Venegas-Martínez

    (Escuela Superior de Economía, Instituto Politécnico Nacional, Mexico City 11350, Mexico)

  • Oscar V. De la Torre-Torres

    (Facultad de Contaduría y Ciencias Administrativas, Universidad Michoacana de San Nicolás de Hidalgo (UMSNH), Morelia 58000, Mexico)

  • José Álvarez-García

    (Departamento de Economía Financiera y Contabilidad, Instituto Universitario de Investigación para el Desarrollo Territorial Sostenible (INTERRA), Facultad de Empresa Finanzas y Turismo, Universidad de Extremadura, Avda. de la Universidad, n° 47, 10071 Caceres, Spain)

Abstract

This paper aims to simulate portfolio decisions under uncertainty when the diffusion parameters of the risky asset and short rate paid for a bond are both modulated by a time-inhomogeneous Markov chain, with transition probabilities dependent on states, time, and asset prices. To do this, we first found closed-form solutions of the corresponding utility-maximization problem, which solves a rational consumer that makes portfolio and consumption decisions by using the corresponding infinitesimal generator associated with the Markov chain. Subsequently, as an illustration of the theoretical results obtained, several scenarios were simulated for the Mexican case. The expected economic policy was inferred from announced monetary policy decisions regarding the reference rate and possible changes in trend due to the lack of fiscal stimuli. Under this framework, states were defined from the current and expected economic policies, and transition probabilities were expressed in terms of the ratio between the prices of the risky asset and the bond. It should be noted, as far as the authors know, that no analytical solutions are known in the literature for the case of Markov-modulated time-inhomogeneous chains with transition probabilities that, themselves, are stochastic processes.

Suggested Citation

  • Benjamín Vallejo-Jiménez & Francisco Venegas-Martínez & Oscar V. De la Torre-Torres & José Álvarez-García, 2022. "Simulating Portfolio Decisions under Uncertainty When the Risky Asset and Short Rate Are Modulated by an Inhomogeneous and Asset-Dependent Markov Chain," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2926-:d:887843
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    References listed on IDEAS

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    4. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    5. Areski Cousin & Ying Jiao & Christian Yann Robert & Olivier David Zerbib, 2022. "Optimal Asset Allocation Subject to Withdrawal Risk and Solvency Constraints," Risks, MDPI, vol. 10(1), pages 1-28, January.
    6. Gapeev, Pavel V., 2022. "Discounted optimal stopping problems in continuous hidden Markov models," LSE Research Online Documents on Economics 110493, London School of Economics and Political Science, LSE Library.
    7. Vasishta Bhargava Nukala & S. S. Prasada Rao, 2021. "Role of debt-to-equity ratio in project investment valuation, assessing risk and return in capital markets," Future Business Journal, Springer, vol. 7(1), pages 1-23, December.
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    1. Monica Aureliana Petcu & Liliana Ionescu-Feleaga & Bogdan-Ștefan Ionescu & Dumitru-Florin Moise, 2023. "A Decade for the Mathematics : Bibliometric Analysis of Mathematical Modeling in Economics, Ecology, and Environment," Mathematics, MDPI, vol. 11(2), pages 1-30, January.

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