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Hamilton-Jacobi-Bellman Equation Arising from Optimal Portfolio Selection Problem

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  • Daniel Sevcovic
  • Cyril Izuchukwu Udeani

Abstract

The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear parabolic partial integral differential equation in an abstract setting are investigated by using the Banach fixed-point theorem, the Fourier transform, and the monotone operators technique.

Suggested Citation

  • Daniel Sevcovic & Cyril Izuchukwu Udeani, 2023. "Hamilton-Jacobi-Bellman Equation Arising from Optimal Portfolio Selection Problem," Papers 2308.02627, arXiv.org.
    • Handle: RePEc:arx:papers:2308.02627
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    File URL: http://arxiv.org/pdf/2308.02627
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    References listed on IDEAS

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    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Daniel Sevcovic & Cyril Izuchukwu Udeani, 2021. "Application of maximal monotone operator method for solving Hamilton-Jacobi-Bellman equation arising from optimal portfolio selection problem," Papers 2104.06115, arXiv.org.
    3. Sona Kilianova & Daniel Sevcovic, 2013. "Transformation Method for Solving Hamilton-Jacobi-Bellman Equation for Constrained Dynamic Stochastic Optimal Allocation Problem," Papers 1307.3672, arXiv.org, revised Jul 2013.
    4. Sona Kilianova & Daniel Sevcovic, 2019. "Dynamic intertemporal utility optimization by means of Riccati transformation of Hamilton-Jacobi Bellman equation," Papers 1903.10065, arXiv.org.
    5. Sona Kilianova & Daniel Sevcovic, 2018. "Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio Optimization," Papers 1810.11619, arXiv.org.
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