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An ε-Optimal Portfolio with Stochastic Volatility

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  • Gabih Abdelali
  • Grecksch Wilfried

Abstract

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.

Suggested Citation

  • Gabih Abdelali & Grecksch Wilfried, 2005. "An ε-Optimal Portfolio with Stochastic Volatility," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 1-14, March.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:1:p:1-14:n:2
    DOI: 10.1515/1569396054027256
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    References listed on IDEAS

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    1. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    2. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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