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

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.