This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or its extensions are generally not available for such...

In Longstaff and Schwartz (2001) a method for American option pricing using simulation and regression is suggested, and since then the method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as in Carriere...

We present a novel approach to address sampling error when discretely approximating a dynamic stochastic programme with a limited finite number of scenarios to represent the underlying path probability distribution. This represents a tentative solution to the problems first identified in our...

We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and...

As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to...

This paper provides a general framework for the quantitative analysis of stochastic dynamic models. We review the convergence properties of some numerical algorithms and available methods to bound approximation errors. We then address the convergence and accuracy properties of the simulated...