This is a book on financial modeling that emphasizes computational aspects. It gives

a unified perspective on derivative pricing and hedging across asset classes and is

addressed to all those who are interested in applications of mathematics to finance:

students, quants and academics.

The book features backward stochastic differential equations (BSDEs), which

are an attractive alternative to the more familiar partial differential equations (PDEs)

for representing prices and Greeks of financial derivatives. First, BSDEs offer the

most unified setup for presenting the financial derivatives pricing and hedging theory

(as reflected by the relative compactness of the book, given its rather wide scope).

Second, BSDEs are a technically very flexible and powerful mathematical tool for

elaborating the theory with all the required mathematical rigor and proofs. Third,

BSDEs are also useful for the numerical solution of high-dimensional nonlinear

pricing problems such as the nonlinear CVA and funding issues which have become