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The usefulness of stochastic dynamic programming has been recognized once it became clear that it can be used as a unifying framework for treating multi-stage or multi-periods stochastic optimization problems. However, just as it is a convenient formalism to formulate such problems it is becoming increasingly clear that it is practically difficult to solve them. The stumbling block being the curse of dimensionality inherent in the numerical solution of such problems when the number of variables increases. There are in fact only few problems one can solve completely. For this reason, there is today a broad range of techniques which are an essential part of stochastic dynamic programming and control kits. It is in such a spirit that computer programs, have been devised, providing a computer aided expertise to the solution of these problems. The intent of our presentation is to concentrate our attention on salient aspects of stochastic dynamic programming and control which are important both for potential applications in finance and insurance. A review of applications can be found in Tapiero 1977, 1988, Bensoussan, Hurst and Naslund 1974, Bensoussan, Kleindorfer and Tapiero 1978, 1980, Sethi and Thompson 1981, Kamien and Schwarz 1981, Malliaris and Brock 1982, Whittle 1982 and many others which are listed in this chapter and in the bibliographical list.
KeywordsDynamic Programming Stochastic Differential Equation Dynamic Optimization Stochastic Control Shadow Price
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