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...

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...

We introduce a numerical method to solve stochastic optimal control problems, which are linear in the control. We facilitate the idea of solving two-point boundary value problems with spline functions in order to solve the resulting dynamic programming equation. We then show how to effectively...

In this paper, European put option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stock price from 3/01/2000 to 30/03/2009 is used and resulting partial differential equation is solved by...

We describe an algorithm that is able to compute the solution of a singular linear difference system under rational expectations. The algorithm uses the Generalized Schur Factorization and is illustrated by a simple example