A Dual Method for Evaluation of Dynamic Risk in Diffusion Processes

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We propose a numerical method for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk evaluation to a simple stochastic control problem where the control is a certain Radon-Nikodym derivative process. By exploring the maximum principle, we show that a piecewise-constant dual control provides a good approximation on a short interval. A dynamic programming algorithm extends the approximation to a finite time horizon. Finally, we illustrate the application of the procedure to financial risk management in conjunction with nested simulation and on a multidimensional portfolio valuation problem.

Original languageEnglish (US)
Article number2020018
JournalESAIM - Control, Optimisation and Calculus of Variations
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


  • Dynamic risk measures
  • Financial risk management
  • Forward-backward stochastic differential equations
  • Stochastic maximum principle


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