Composition of approximations of two SDEs with jumps with non-finite Lévy measures. - HAL UNIV-PARIS8 - open access Access content directly
Preprints, Working Papers, ... Year : 2023

Composition of approximations of two SDEs with jumps with non-finite Lévy measures.

Abstract

The purpose of this paper is to extend the results of [13] and [20] concerning the approximation of the solution of some nonlinear second order stochastic PDEs like those satisfied by a consistent dynamic utilities, see [9, 18]. Indeed, in this works, authors showed that the solution of a SPDE of this class is the compound of two monotonic stochastic flows satisfying two SDE. The objective is then to take advantage of this representation to establish a numerical scheme approximating the SPDE's solution using Euler's approximations of the two stochastic flows. This allows us to avoid a complicated discretization in time and space of the SPDE for which it seems really difficult to obtain error estimates. The case where the two flows are solutions of two time-continuous SDEs has been treated in [13] and then extended to the framework with jumps but with a finite Lévy measure in [20]. In the case where the measure is infinite, additional terms specific to the truncation method will appear in our error estimates. In many cases, an optimal choice of parameters allows us to find a convergence rate equal to those established in [13] and [20]. However we provide some examples of Lévy measures with much slower convergence rate.
Fichier principal
Vignette du fichier
HAL_Compound_map_Jumps.pdf (485.31 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04040355 , version 1 (22-03-2023)

Identifiers

  • HAL Id : hal-04040355 , version 1

Cite

Mohamed Mrad, Alexandre Popier. Composition of approximations of two SDEs with jumps with non-finite Lévy measures.. 2023. ⟨hal-04040355⟩
80 View
39 Download

Share

Gmail Mastodon Facebook X LinkedIn More