We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition holds (see Assumption (A) below), we prove existence and uniqueness results under Lipschitz conditions on the coefficients. Some counter examples show that our assumptions are indeed needed. We use a novel approach that allows reduction to a (finite or infinite) system of deterministic differential equations, thus avoiding the use of martingale representation theorems and allowing potential use of standard numerical methods. Finally, we apply the main results to solve an optimal control problem for a marked point process, formulated in a classical way.
|Titolo:||Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control|
FUHRMAN, MARCO ALESSANDRO (Secondo)
|Parole Chiave:||Backward stochastic differential equations; Marked point processes; Stochastic optimal control; Statistics and Probability;|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||10.1214/15-AAP1132|
|Appare nelle tipologie:||01 - Articolo su periodico|