Tutorial for Viscosity Solutions in Optimal Control of Diffusions

36 Pages Posted: 5 Apr 2010 Last revised: 9 Nov 2011

See all articles by Georgios Aivaliotis

Georgios Aivaliotis

University of Leeds - School of Mathematics

Jan Palczewski

University of Leeds - School of Mathematics

Date Written: March 31, 2010

Abstract

This tutorial is an introduction to the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations/inequalities in the realm of stochastic control problems. It is an easy to use reference for application-oriented users of this theory. The presentation is based mainly on the book Pham (2009) "Continuous-time Stochastic Control and Optimization with Financial Applications", but borrows from many other references as well. What sets it apart from existing publications is the devotion to details and avoidance of "hand-waving". In particular, all assumptions are clearly stated and proofs are presented in a complete form.

Keywords: viscosity solutions, optimal control, diffusion, Hamilton-Jacobi-Bellman, variational inequality

JEL Classification: C00

Suggested Citation

Aivaliotis, Georgios and Palczewski, Jan, Tutorial for Viscosity Solutions in Optimal Control of Diffusions (March 31, 2010). Available at SSRN: https://ssrn.com/abstract=1582548 or http://dx.doi.org/10.2139/ssrn.1582548

Georgios Aivaliotis

University of Leeds - School of Mathematics ( email )

Leeds LS2 9JT
United Kingdom

Jan Palczewski (Contact Author)

University of Leeds - School of Mathematics ( email )

Leeds, LS2 9JT
United Kingdom

HOME PAGE: http://www.maths.leeds.ac.uk/~jp

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