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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4951 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4951 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4951 archive 351 disk0/00/00/70/50 2016-01-15 02:15:54 2021-08-27 17:18:21 2016-01-15 02:15:54 monograph show 2 Ermoliev Y.M. 1445 Norkin V.I. AL1055 pub iis_ecn iis_met iis_rsp prog_ins The proper analysis of policies under uncertainties has to deal with "hit-or-miss" type situations by using approximate risk functions, which can also be viewed as so-called extended expected utility functions. Formally this often requires the solution of dynamic stochastic optimization problems with discontinuous indicator functions of such events as ruin, underestimating costs and overestimating benefits. The available optimization techniques, in particular formulas for derivatives of risk functions, may not be applicable due to explicitly unknown probability distributions and essential discontinuities. The aim of this paper is to develop a solution technique by smoothing the risk function over certain parameters, rather than over decision variables as in the classical distribution (generalized functions) theory. For smooth approximations we obtain gradients in the form of expectations of stochastic vectors which can be viewed as a form of stochastic gradients for the original risk function. We pay special attention to optimization of risk functions defined on trajectories of discrete time stochastic processes with stopping times, which is critically important for analyzing regional vulnerability against catastrophes. 2003-08 published IR-03-033 IR-03-033 338 2245 public interim_report IIASA, Laxenburg, Austria 23 FALSE info:eu-repo/semantics/book