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. AMS Subject Classification: 91B51, 62M10, 91G20, 65C05 Received: March 17, 2015 c © 2015 Academic Publications, Ltd. url: www.acadpubl.eu §Correspondence author 712 Ma. T.V. Martinez-Palacios, F. Venegas-Martinez, J.M. Sanchez
Highlights
The contingent reality faced by different economic agents participating in the various financial markets impacts their decision making on consumption and portfolio
In order to model this kind of decision making in risky environments, sophisticated mathematical tools have been developed in recent years with a boost up
Particular attention has been paid to the theoretical approach of dynamic stochastic general equilibrium models (DSGEM)
Summary
The contingent reality faced by different economic agents participating in the various financial markets impacts their decision making on consumption and portfolio. Generalizations of the Black and Scholes’ (1973) partial differential equation are the most widely used mathematical models to value derivatives This allows, depending on the nature of the imposed boundary conditions, obtaining the theoretical price of different derivatives available in financial markets (exchanges and over-the-counter). In this context, it is important to extend the B&S model by introducing stochastic volatility of the underlying asset. The distinguishing features of this research, with respect to the above investigations are: 1) the planning horizon is finite but with stochastic length, 2) the stopping time process avoids degenerate solutions and is helpful in modeling an American derivative, and 3) the valuation of the American option is carried out through the Monte-Carlo method.
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