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 investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic...

A numerical method for solving a class of fractional optimal control problems (FOCPs) is presented. First, the FOCP is transformed into an equivalent variational problem, then using Lagrange polynomials, the problem is reduced to the problem of solving a system of algebraic equations. With the...

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, we investigate model-independent bounds for option prices given market instruments.This super-replication problem can be written as a semi-infinite linear programming problem. As these super-replication prices can be large and the densities Q which achieve the upper bounds quite...