Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: By applying stochastic dynamic programming to the minimization of a mean-squared error loss function under Markov-state dynamics, recursive expressions for the optimal-replication strategy are derived that are readily implemented in practice.
Abstract: Given a European derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based, we solve the optimal-replication problem: Find a self-financing dynamic portfolio strategy--involving only the underlying securities--that most closely approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a mean-squared error loss function under Markov-state dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or "e" of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. To investigate the practical significance of these e-arbitrage strategies, we consider several numerical examples, including path-dependent options and options on assets with stochastic volatility and jumps.
149 citations
••
TL;DR: The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.
Abstract: This paper deals with two mathematically similar problems in transport network analysis: trip matrix estimation and traffic signal optimisation on congested road networks. These two problems are formulated as bi-level programming problems with stochastic user equilibrium assignment as the second-level programming problem. We differentiate two types of solutions in the combined matrix estimation and stochastic user equilibrium assignment problem (or the combined signal optimisation and stochastic user equilibrium assignment problem): one is the solution to the bi-level programming problem and the other the mutually consistent solution where the two sub-problems in the combined problem are solved simultaneously. In this paper, we shall concentrate on the bi-level programming approach, although we shall also consider mutually consistent solutions so as to contrast the two types of solutions. The purpose of the paper is to present a solution algorithm for the two bi-level programming problems and to test the algorithm on several networks.
149 citations
••
TL;DR: A linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value is O(log3/2n), and anΩ(1) lower bound on the expected Difference between the optimal and the solution found by any on- line algorithm is shown to hold.
Abstract: Different classes of on-line algorithms are developed and analyzed for the solution of {0, 1} and relaxed stochastic knapsack problems, in which both profit and size coefficients are random variables. In particular, a linear time on-line algorithm is proposed for which the expected difference between the optimum and the approximate solution value isO(log3/2
n). AnΩ(1) lower bound on the expected difference between the optimum and the solution found by any on-line algorithm is also shown to hold.
149 citations
••
TL;DR: This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers to these problems.
Abstract: This paper presents consistency results for sequences of optimal solutions to convex stochastic optimization problems constructed from empirical data, by applying the strong law of large numbers fo...
149 citations
••
TL;DR: Two-stage stochastic programming approach is used to minimize the operational cost in microgrid energy management and a scenario reduction method based on mixed-integer linear optimization is obtained.
149 citations