IJPAM: Volume 104, No. 3 (2015)

OPTIMAL CONSUMPTION AND PORTFOLIO DECISIONS
WHEN THE RISKY ASSET IS DRIVEN BY
A TIME-INHOMOGENEOUS MARKOV
MODULATED DIFFUSION PROCESS

Benjamín Vallejo-Jiménez$^1$, Francisco Venegas-Martínez$^2$,
Yazmín Viridiana Soriano-Morales$^3$
$^{1,2,3}$Escuela Superior de Economía of the Instituto Politécnico Nacional
Plan de Agua Prieta No. 66, Miguel Hidalgo
C.P. 11340
Mexico City, MÉXICO


Abstract. This research is aimed at finding closed-form solutions of the utility maximization problem that solves an infinitely-lived rational consumer when the risky asset is driven by a time-inhomogeneous Markov modulated diffusion process. We provide analytical solutions for two specific cases: transition probabilities with tendency and transition probabilities with no tendency and no periodicity.

Received: June 8, 2015

AMS Subject Classification: 35F21, 60J27, 60G50, 60J60

Key Words and Phrases: diffusion processes, Hamilton–Jacobi–Bellman equation, continuous-time Markov processes

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DOI: 10.12732/ijpam.v104i3.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 104
Issue: 3
Pages: 353 - 362


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