We treat financial mathematical models driven by noise of Lévy type in the framework of the backward stochastic differential 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 financial data and classical models which are based on Brownian diffusions. BSEDs' techniques in presence of Lévy 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 Lévy 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 Lévy driven BSDEs, making use of the concept of g − expectation in presence of a Lipschitz driver.