2 citations · 4 across the 4 of their papers we have counts for
6 papers
Full-Projection explicit FBSDE scheme for parabolic PDEs with superlinear nonlinearities
Arnaud Lionnet, Gonçalos dos Reis, Lukasz Szpruch
Developing efficient and stable approximations for high dimensional PDEs is of key importance for numerous applications. The language of Forward-Backward Stochastic Differential Eq…
Adapted time steps explicit scheme for monotone BSDEs
Arnaud Lionnet
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…
Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth
Arnaud Lionnet, Gonçalo dos Reis, Lukasz Szpruch
The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results o…
Equilibrium pricing under relative performance concerns
Jana Bielagk, Arnaud Lionnet, Goncalo Dos Reis
We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced…
Time discretization of FBSDE with polynomial growth drivers and reaction-diffusion PDEs
Arnaud Lionnet, Gonçalo dos Reis, Lukasz Szpruch
In this paper, we undertake the error analysis of the time discretization of systems of Forward-Backward Stochastic Differential Equations (FBSDEs) with drivers having polynomial g…
Some results on general quadratic reflected BSDEs driven by a continous martingale
Arnaud Lionnet
We study the well-posedness of general reflected BSDEs driven by a continuous martingale, when the coefficient f of the driver has at most quadratic growth in the control variable…