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Portfolio Optimization with Allocation Constraints and Stochastic Factor Market Dynamics

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  • Marcos Escobar-Anel
  • Michel Kschonnek
  • Rudi Zagst

Abstract

We study the expected utility portfolio optimization problem in an incomplete financial market where the risky asset dynamics depend on stochastic factors and the portfolio allocation is constrained to lie within a given convex set. We employ fundamental duality results from real constrained optimization to formally derive a dual representation of the associated HJB PDE. Using this representation, we provide a condition on the market dynamics and the allocation constraints, which ensures that the solution to the HJB PDE is exponentially affine and separable. This condition is used to derive an explicit expression for the optimal allocation-constrained portfolio up to a deterministic minimizer and the solution to a system of Riccati ODEs in a market with CIR volatility and in a market with multi-factor OU short rate.

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  • Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2023. "Portfolio Optimization with Allocation Constraints and Stochastic Factor Market Dynamics," Papers 2303.09835, arXiv.org.
    • Handle: RePEc:arx:papers:2303.09835
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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.
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    1. M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.

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