O PTIMAL SCENARIO TREE REDUCTION FOR FINANCIAL OPTIMIZATION PROBLEMSDiana Barro1,Elio Canestrelli1and Pierangelo Ciurlia11Department of Applied MathematicsUniversity Ca’Foscari Venice(e-mail:d.barro@unive.it,canestre@unive.it,ciurlia@unive.it)A BSTRACT:The solution of a multistage stochastic programming problem needs a suitable representation of uncertainty which may be obtained through a satisfactory scenario tree con-struction.Unfortunately there is a trade-off between the level of accuracy in the description of the stochastic component and the computational tractability of the resulting scenario-based problem.In this contribution we address the problem of how to face such a trade-off which plays a crucial role in the determination of the optimal solution.To this aim we discuss meth-ods which allow to progressively reduce a given scenario tree by means of state aggregation.In this process it is important to take into account the choice of proper aggregation criteria in order to try to preserve all the relevant information.K EYWORDS:Stochastic Programming,Scenario tree,Reduction,Spatial Aggregation.1IntroductionA possible way to cope with uncertainty in multiperiodfinancial optimization prob-lems is to use scenarios to describe the possible future market situations.The introduc-tion of a scenario tree structure to describe uncertainty allows to transform a stochastic programming problem into a deterministic equivalent optimization problem.Although the resulting scenario-based problem represents an approximation of the original stochastic problem,it may still be difficult to solve directly due to its large dimensions.To deal with this difficulty we can resort to either proper optimiza-tion methods,which exploit the structure of the problem(see among others Barro& Canestrelli,2005a),or aggregation techniques which reduce the dimensions of the original scenario tree.The construction of a scenario tree is a complex task which requires not only the modelling of the random data and the estimation of the underlying stochastic processes,but also the choice of proper discretization,approximation or sampling techniques.In this contribution we focus only on the problem of the reduction of a given scenario tree for a multistage portfolio model.We are interested in reducing the dimensions,i.e.the number of scenarios,of the original scenario tree in order to obtain a smaller tree while preserving as much of the information content as possible.In more detail we are interested in the distance between the two scenario trees,the original one and the reduced one,with respect
本文来源：https://www.2haoxitong.net/k/doc/698efd0a581b6bd97f19ea62.html
