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FBSDE approach to utility portfolio selection in a market with random parameters

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  • Ferland, René
  • Watier, François

Abstract

A continuous-time utility portfolio selection problem is studied in a market in which the interest rate, appreciation rates and volatility coefficients are driven by Brownian motion. We construct an optimal portfolio using results from forward-backward stochastic differential equations (FBSDE) theory. As an illustration, exact computation of the optimal strategy is done for the power and exponential type utilities.

Suggested Citation

  • Ferland, René & Watier, François, 2008. "FBSDE approach to utility portfolio selection in a market with random parameters," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 426-434, March.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:4:p:426-434
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    References listed on IDEAS

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    1. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    2. Andrew E. B. Lim, 2004. "Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 132-161, February.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. 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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    Cited by:

    1. Ali Al-Aradi & Sebastian Jaimungal, 2020. "A Variational Analysis Approach to Solving the Merton Problem," Papers 2003.08450, arXiv.org.

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