13,631 research outputs found
Numerical Schemes for Multivalued Backward Stochastic Differential Systems
We define some approximation schemes for different kinds of generalized
backward stochastic differential systems, considered in the Markovian
framework. We propose a mixed approximation scheme for a decoupled system of
forward reflected SDE and backward stochastic variational inequality. We use an
Euler scheme type, combined with Yosida approximation techniques.Comment: 13 page
A numerical algorithm for fully nonlinear HJB equations: an approach by control randomization
We propose a probabilistic numerical algorithm to solve Backward Stochastic
Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs
introduced in [9] for representing fully nonlinear HJB equations. In
particular, this allows us to numerically solve stochastic control problems
with controlled volatility, possibly degenerate. Our backward scheme, based on
least-squares regressions, takes advantage of high-dimensional properties of
Monte-Carlo methods, and also provides a parametric estimate in feedback form
for the optimal control. A partial analysis of the error of the scheme is
provided, as well as numerical tests on the problem of superreplication of
option with uncertain volatilities and/or correlations, including a detailed
comparison with the numerical results from the alternative scheme proposed in
[7]
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