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Dynamic intertemporal utility optimization by means of Riccati transformation of Hamilton-Jacobi Bellman equation

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  • Sona Kilianova
  • Daniel Sevcovic

Abstract

In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati method for transformation of the fully nonlinear HJB equation into a quasi-linear parabolic equation with non-local terms involving the intertemporal utility function. As a numerical method we propose a semi-implicit scheme in time based on a finite volume approximation in the spatial variable. By analyzing an explicit traveling wave solution we show that the numerical method is of the second experimental order of convergence. As a practical application we compute optimal strategies for a portfolio investment problem motivated by market financial data of German DAX 30 Index and show the effect of considering intertemporal utility on optimal portfolio selection.

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  • Sona Kilianova & Daniel Sevcovic, 2019. "Dynamic intertemporal utility optimization by means of Riccati transformation of Hamilton-Jacobi Bellman equation," Papers 1903.10065, arXiv.org.
    • Handle: RePEc:arx:papers:1903.10065
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    References listed on IDEAS

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    1. Sid Browne, 2000. "Risk-Constrained Dynamic Active Portfolio Management," Management Science, INFORMS, vol. 46(9), pages 1188-1199, September.
    2. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
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    Cited by:

    1. 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.
    2. Daniel Sevcovic & Cyril Izuchukwu Udeani, 2023. "Hamilton-Jacobi-Bellman Equation Arising from Optimal Portfolio Selection Problem," Papers 2308.02627, arXiv.org.
    3. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.

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