The paper surveys the basic results and nonresults for decision rules in stochastic programming. ... more The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms. A liberal dosage of examples is provided which illustrate various cases. The treatment is unified by making use of the equivalence of various formulations
Summary An analysis of the topology generated by the ρ-hausdorff distances on the hyperspace of s... more Summary An analysis of the topology generated by the ρ-hausdorff distances on the hyperspace of subsets of a normed linear space. In addition, a compactness criterion is derived for the topology generated by the pointwise convergence of the distance functions (the Choquet-Wijsman topology).
We develop a general framework for the study and the control of the eutrophication process of (sh... more We develop a general framework for the study and the control of the eutrophication process of (shallow) lakes. The randomness of the environment (variability in hydrological and meteorological conditions) is an intrinsic characteristic of such systems that cannot be ignored in the analysis of the process or by management in the design of control measures.
Abstract Several exponential bounds are derived by means of the theory of large deviations for th... more Abstract Several exponential bounds are derived by means of the theory of large deviations for the convergence of approximate solutions of stochastic optimization problems. The basic results show that the solutions obtained by replacing the original distribution by an empirical distribution provides an effective tool for solving stochastic programming problems.
In this paper, a new algorithm for contingent claims pricing is proposed by the operational duali... more In this paper, a new algorithm for contingent claims pricing is proposed by the operational duality in the preceding paper and a novel estimate approach. The duality can guide us how to discretize our pricing problem with contin- uous distributions ecien tly if the distributions are known, and by our novel approach we can estimate the distributions from historical data, which is specially useful for the computation. We present experimental results from applying this algorithm to some practical examples that demonstrate the reasonability and eciency of our new algorithm.
... supported by the US National Science Foundation under grant DMS 0205699 and Office of Naval ... more ... supported by the US National Science Foundation under grant DMS 0205699 and Office of Naval Research under grant MURI N00014 ... To generate the kernel-estimators we relied on theCRAN package of the R Foundation of Statistical Computing always computing first the ...
A generalized approach is taken to linear and quadratic programming in which dual as well as prim... more A generalized approach is taken to linear and quadratic programming in which dual as well as primal variables may be subjected to bounds, and constraints may be represented through penalties. Corresponding problem models in optimal control related to continuous-time programming are then set up and theorems on duality and the existence of solutions are derived. Optimality conditions are obtained in the form of a global saddle point property which decomposes into an instantaneous saddle point condition on the primal and dual control vectors at each time, along with an endpoint condition.
Stability in Two-Stage Stochastic Programming. [SIAM Journal on Control and Optimization 25, 1409... more Stability in Two-Stage Stochastic Programming. [SIAM Journal on Control and Optimization 25, 1409 (1987)]. Stephen M. Robinson, Roger J.-B. Wets. Abstract. We analyze the effect of changes in problem functions and/or distributions ...
Two fundamental classes of problems in large-scale linear and quad- ratic programming are describ... more Two fundamental classes of problems in large-scale linear and quad- ratic programming are described. Multistage problems covering a wide variety of models in dynamic programming and stochastic programming are represented in a new way. Strong properties of duality are revealed which support the devel- opment of iterative approximate techniques of solution in terms of saddlepoints. Optimality conditions are derived in
Necessary and sufficient conditions for optimality are derived for multistage stochastic programs... more Necessary and sufficient conditions for optimality are derived for multistage stochastic programs. In particular it is shown that under some standard regularity conditions and a condition of “nonanticipative feasibility”, a system of Lagrange multipliers, characterized by a martingale property, can be associated with the constraints of the problem. Nonanticipative feasibility is expressed in terms of the nonanticipativity of a certain
The paper surveys the basic results and nonresults for decision rules in stochastic programming. ... more The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms. A liberal dosage of examples is provided which illustrate various cases. The treatment is unified by making use of the equivalence of various formulations
Summary An analysis of the topology generated by the ρ-hausdorff distances on the hyperspace of s... more Summary An analysis of the topology generated by the ρ-hausdorff distances on the hyperspace of subsets of a normed linear space. In addition, a compactness criterion is derived for the topology generated by the pointwise convergence of the distance functions (the Choquet-Wijsman topology).
We develop a general framework for the study and the control of the eutrophication process of (sh... more We develop a general framework for the study and the control of the eutrophication process of (shallow) lakes. The randomness of the environment (variability in hydrological and meteorological conditions) is an intrinsic characteristic of such systems that cannot be ignored in the analysis of the process or by management in the design of control measures.
Abstract Several exponential bounds are derived by means of the theory of large deviations for th... more Abstract Several exponential bounds are derived by means of the theory of large deviations for the convergence of approximate solutions of stochastic optimization problems. The basic results show that the solutions obtained by replacing the original distribution by an empirical distribution provides an effective tool for solving stochastic programming problems.
In this paper, a new algorithm for contingent claims pricing is proposed by the operational duali... more In this paper, a new algorithm for contingent claims pricing is proposed by the operational duality in the preceding paper and a novel estimate approach. The duality can guide us how to discretize our pricing problem with contin- uous distributions ecien tly if the distributions are known, and by our novel approach we can estimate the distributions from historical data, which is specially useful for the computation. We present experimental results from applying this algorithm to some practical examples that demonstrate the reasonability and eciency of our new algorithm.
... supported by the US National Science Foundation under grant DMS 0205699 and Office of Naval ... more ... supported by the US National Science Foundation under grant DMS 0205699 and Office of Naval Research under grant MURI N00014 ... To generate the kernel-estimators we relied on theCRAN package of the R Foundation of Statistical Computing always computing first the ...
A generalized approach is taken to linear and quadratic programming in which dual as well as prim... more A generalized approach is taken to linear and quadratic programming in which dual as well as primal variables may be subjected to bounds, and constraints may be represented through penalties. Corresponding problem models in optimal control related to continuous-time programming are then set up and theorems on duality and the existence of solutions are derived. Optimality conditions are obtained in the form of a global saddle point property which decomposes into an instantaneous saddle point condition on the primal and dual control vectors at each time, along with an endpoint condition.
Stability in Two-Stage Stochastic Programming. [SIAM Journal on Control and Optimization 25, 1409... more Stability in Two-Stage Stochastic Programming. [SIAM Journal on Control and Optimization 25, 1409 (1987)]. Stephen M. Robinson, Roger J.-B. Wets. Abstract. We analyze the effect of changes in problem functions and/or distributions ...
Two fundamental classes of problems in large-scale linear and quad- ratic programming are describ... more Two fundamental classes of problems in large-scale linear and quad- ratic programming are described. Multistage problems covering a wide variety of models in dynamic programming and stochastic programming are represented in a new way. Strong properties of duality are revealed which support the devel- opment of iterative approximate techniques of solution in terms of saddlepoints. Optimality conditions are derived in
Necessary and sufficient conditions for optimality are derived for multistage stochastic programs... more Necessary and sufficient conditions for optimality are derived for multistage stochastic programs. In particular it is shown that under some standard regularity conditions and a condition of “nonanticipative feasibility”, a system of Lagrange multipliers, characterized by a martingale property, can be associated with the constraints of the problem. Nonanticipative feasibility is expressed in terms of the nonanticipativity of a certain
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Papers by Roger Wets