Approximation Schemes for Mixed Optimal Stopping and Control Problems with Nonlinear Expectations and Jumps

Roxana Dumitrescu, Christoph Reisinger, Yufei Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
122 Downloads (Pure)

Abstract

We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems, piecewise constant policy timestepping reduces the problem to nonlocal semi-linear equations with different control parameters, uncoupled over individual time steps, which we solve by fully implicit monotone approximations to the controlled diffusion and the nonlocal term, and specifically the Lax–Friedrichs scheme for the nonlinearity in the gradient. We establish a comparison principle for the switching system and demonstrate the convergence of the schemes, which subsequently gives a constructive proof for the existence of a solution to the switching system. Numerical experiments are presented for a recursive utility maximization problem to demonstrate the effectiveness of the new schemes.

Original languageEnglish
Number of pages43
JournalAPPLIED MATHEMATICS AND OPTIMIZATION
Volume2019
Early online date5 Jul 2019
DOIs
Publication statusE-pub ahead of print - 5 Jul 2019

Keywords

  • Approximation schemes
  • Jump processes
  • Nonlinear expectations
  • Optimal stopping
  • Piecewise constant policy timestepping
  • Stochastic control

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