Piecewise constant policy approximations to Hamilton-Jacobi-Bellman equations

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• 作者：C. Reisinger^a ; ^{reisinge@maths.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; P.A. Forsyth^b ; ^{paforsyt@uwaterloo.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fully nonlinear PDEs ; Monotone approximation schemes ; Piecewise constant policy time stepping ; Viscosity solutions ; Uncertain volatility model ; Mean variance
• 刊名：Applied Numerical Mathematics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：103
• 期：Complete
• 页码：27-47
• 全文大小：759 K

文摘

An advantageous feature of piecewise constant policy timestepping for Hamilton–Jacobi–Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control parameters. Standard convergence analysis suggests that monotone (i.e., linear) interpolation must be used to transfer data between meshes. Using the equivalence to a switching system and an adaptation of the usual arguments based on consistency, stability and monotonicity, we show that if limited, potentially higher order interpolation is used for the mesh transfer, convergence is guaranteed. We provide numerical tests for the mean-variance optimal investment problem and the uncertain volatility option pricing model, and compare the results to published test cases.