Adapted time steps explicit scheme for monotone BSDEs
For researchers in numerical analysis of BSDEs, this provides a practical solution to stability issues in explicit schemes, though it is an incremental improvement over existing methods.
The paper addresses numerical instability in explicit schemes for BSDEs with monotone drivers, proposing an adapted time-step method that guarantees strong stability and convergence, validated by simulations.
We study the numerical strong stability of explicit schemes for the numerical approximation of the solution to a BSDE where the driver has polynomial growth in the primary variable and satisfies a monotone decreasing condition, and we introduce an explicit scheme with adapted time-steps that guarantee numerical strong stability. We then prove the convergence of this scheme and illustrate it with numerical simulations.