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

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 fu...

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Bibliographic Details
Published in:	Japan journal of industrial and applied mathematics Vol. 30; no. 1; pp. 51 - 67
Main Authors:	Ishimura, Naoyuki, Ševčovič, Daniel
Format:	Journal Article
Language:	English
Published:	Japan Springer Japan 01-02-2013 Springer Nature B.V
Subjects:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Original Paper 70H20 Hamilton–Jacobi–Bellman equation 91B16 Stochastic dynamic programming 91B70 90C15 Riccati transformation Traveling wave solution 35K55 34E05
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Summary:	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.
ISSN:	0916-7005 1868-937X
DOI:	10.1007/s13160-012-0087-8