We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and La-grangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

A number of methods for solving multistage stochastic linear programs with recourse decompose the deterministic equivalent [4] to form subproblems based on scenarios (e.g., Rockafellar and Wets [6] and Mulvey and Ruszczyński [5]). Other methods use forms of Benders decomposition to form subproblems based on nodes of the scenario tree (e.g., Birge [1] and Gassmann [2]). Both types of algorithms ...

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establi...

It is well known that risk-averse multistage stochastic optimization problems are often not in the form of a dynamic stochastic program, i.e. are not dynamically decomposable. In this paper we demonstrate how some of these problems may be extended in such a way that they are accessible to dynamic algorithms. The key technique is a new recursive formulation for the Average Value-atRisk. To this ...

This paper is concerned with modeling p lann ing problems invo lv ing uncerta inty as d iscre tet ime, f in i te -s ta le stochastic au toma ta So lv ing p l ann ing problems is reduced to comp u t i n g policies for Markov decision processes Classical methods for solv ing Markov decision processes cannot cope w i t h the size of the state spaces for typ ica l problems encountered in pract ice ...

Abstract. We show that for a quantum L-martingale (X(t)), p > 2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|). A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an L-martingale, p > 2, is constructed. Using this construction, the uniqueness of the Doob-Me...

We address the problems of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. We show that when volatility is stochastic but fast mean reverting Black-Scholes pricing theory can be corrected. The correction accounts for the effect of stochastic volatility and the associated market price of risk. For European derivatives it is given by explic...

In the “statistical theory of signal detection,’’ as I understand the phrase, we are concerned with problems occurring in electrical communication engineering involving statistical inference from stochastic processes. Most of the work in this area has been directed to the theory of detecting or characterizing information-bearing signals immersed in noise with Gaussian statistics. It is one aspe...

Generalized polynomial chaos (gPC) methods have been successfully applied to various stochastic problems in many physical and engineering fields. However, realistic representation of stochastic inputs associated with various sources of uncertainty often leads to high dimensional representations that are computationally prohibitive for classic gPC methods. Additionally in the classic gPC methods...

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the stochastic cellular automaton evolution. The s...