Consumption and portfolio decisions of a rational agent that has access to an American put option on an underlying asset with stochastic volatility

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.