Forward–Backward SDEs Driven by Lévy Process in Stopping Time Duration

Abstract

As the first part in the present paper, we study a class of backward stochastic differential equation (BSDE, for short) driven by Teugels martingales associated with some Lévy processes having moment of all orders and an independent Brownian motion. We obtain an existence and uniqueness result for this type of BSDEs when the final time is allowed to be random. As the second part, we prove, under a monotonicity condition, an existence and uniqueness result for fully coupled forward–backward stochastic differential equation (FBSDE, for short) driven by Teugels martingales in stopping time duration. As an illustration of our theoretical results, we deal with a portfolio selection in Lévy-type market.

Keywords

Forward–backward stochastic differential equations / Teugels martingale / Lévy process / Stopping time

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