We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a 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  risk management in conjunction with nested simulation  .
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a 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 an multidimensional portfolio valuation problem .
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financial
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and on an multidimensional portfolio valuation problem