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We consider an extended Merton's problem of optimal consumption and investment in continuous-time with stochastic volatility. The wealth process of the investor is approximated by a particular weak Itô-Taylor approximation called Euler scheme. It is shown that the optimal control of the value function generated by the Euler scheme is an ε-optimal control of the original problem of maximizing total expected discounted HARA utility from consumption.
Key Words: Stochastic volatility,; portfolio optimization,; ε-optimal control,; time-discrete approximation.
Published Online: --
Published in Print: 2005-03-01
Copyright 2005, Walter de Gruyter
