Abstract
We investigate numerical methods for forward-backward stochastic differential equations driven by a Brownian motion and a compensated Poisson random measure. We consider three approaches to solving FBSDEs. We apply discrete-time approximations and we derive recursive representations of the solution involving conditional expected values. In order to estimate the conditional expected values, we use Least Squares Monte Carlo which overcomes nested Monte Carlo simulations. In the case of a FBSDE driven by a Brownian motion and a compensated Poisson process we replace the original driving noises by discrete-space martingales. We also use the connection with partial integro-differential equations and we present an explicit-implicit finite difference method for solving a PIDE.
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Delong, Ł. (2013). Numerical Methods for FBSDEs. In: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-5331-3_5
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DOI: https://doi.org/10.1007/978-1-4471-5331-3_5
Publisher Name: Springer, London
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