Backward Stochastic Differential Equations Driven by Levy Noise with Applications in Finance

Abstract

The main goal of this paper is to provide a coincise and self- contained introduction to treat nancial mathematical models driven by noise of L evy type in the framework of the backward stochastic di erential equations (BSDEs) theory. We shall present techniques and results which are relevant from a mathematical point of views as well in concrete market applications, since they allow to overcome the discrepancies between real world nancial data and classical models which are based on Brownian di usions. BSEDs' techniques in presence of L evy perturbations actually play a major role in the solution of hedging and pricing problems especially with respect to non-linear scenarios and for incomplete markets. In particular, we provide an analogue of the celebrated Black{Scholes formula, but the L evy market case, with a clear economical interpretation for all the involved nancial parameters, as well as an introduction to the emerging eld of dynamic risk measures, for L evy driven BSDEs, making use of the concept of g-expectation in presence of a Lipschitz driver.