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Value-at-risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model

Author

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  • Marcos Escobar-Anel

    (Western University)

  • Yevhen Havrylenko

    (Technical University of Munich
    University of Copenhagen
    Ulm University)

  • Rudi Zagst

    (Technical University of Munich)

Abstract

We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic programming approach. We demonstrate that the value function in the constrained problem can be represented as the expected modified utility function of a vega-neutral financial derivative on the optimal terminal wealth in the unconstrained utility-maximization problem. Via the same financial derivative, the optimal wealth and the optimal investment strategy in the constrained problem are linked to the optimal wealth and the optimal investment strategy in the unconstrained problem. In numerical studies, we substantiate the impact of risk aversion levels and investment horizons on the optimal investment strategy. We observe a $$20\%$$ 20 % relative difference between the constrained and unconstrained allocations for average parameters in a low-risk-aversion short-horizon setting.

Suggested Citation

  • Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2025. "Value-at-risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston’s model," Annals of Operations Research, Springer, vol. 347(3), pages 1265-1309, April.
    • Handle: RePEc:spr:annopr:v:347:y:2025:i:3:d:10.1007_s10479-024-06390-x
    DOI: 10.1007/s10479-024-06390-x
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