Ma. Teresa V. Martínez-Palacios, Francisco Venegas-Martínez,
José Francisco Martínez Sánchez
Escuela Superior de Apan
Universidad Autónoma del Estado de Hidalgo
Carretera Apan-Calpulalpan Km. 8
Col. Chimalpa, 43920 Apan, Hgo. MEXICO
Escuela Superior de Economía
Instituto Politécnico Nacional (ESE-IPN)
Plan de Agua Prieta 66, Plutarco Elías Calles
Miguel Hidalgo, 11350 Ciudad de México, D.F., MEXICO
Escuela Superior de Apan
Universidad Autónoma del Estado de Hidalgo
Carretera Apan-Calpulalpan Km. 8
Col.Chimalpa, 43920 Apan, Hgo. MEXICO

Abstract. This paper is aimed at developing a model of a risk-averse rational consumer that has an initial wealth and faces the decision to allocate his wealth between consumption and investment in a portfolio of assets in a finite time horizon of stochastic length, so as to maximize his/her expected total utility. Particularly, the agent may invest in an American put option on an asset with stochastic volatility. Finally, the valuation of the American put option is carried out by using the Monte Carlo method.

Received: March 17, 2015

AMS Subject Classification: 91B51, 62M10, 91G20, 65C05

Key Words and Phrases: continuous time stochastic optimal control, stochastic volatility, American contingent claims, Monte Carlo simulation

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