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On traveling wave solutions to Hamilton-Jacobi-Bellman equation with inequality constraints

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  • Naoyuki Ishimura
  • Daniel Sevcovic

Abstract

The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct monotone traveling wave solutions and identify parametric regions for which the traveling wave solution has a positive or negative wave speed.

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  • Naoyuki Ishimura & Daniel Sevcovic, 2011. "On traveling wave solutions to Hamilton-Jacobi-Bellman equation with inequality constraints," Papers 1108.1035, arXiv.org, revised May 2012.
    • Handle: RePEc:arx:papers:1108.1035
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    References listed on IDEAS

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    1. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    2. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    3. Zuzana Macova & Daniel Sevcovic, 2009. "Weakly nonlinear analysis of the Hamilton-Jacobi-Bellman equation arising from pension savings management," Papers 0905.0155, arXiv.org, revised Nov 2009.
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