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Convexity in stochastic programming model with indicators of ecological stability
Houda, Michal
We develop an optimization model dealing with construction expenses that are prescribed as a result of the EIA (Environmental Impact Assessment) process. The process is an obligatory part of every large construction project and evaluates possible influences of the project to the environment, including population health, natural and other socio-economic aspects; the result of the process is a set of recommendation and arrangements the construction must meet. Our optimization model incorporates uncertainties in model parameters; we represent them through their probabilistic distribution. Furthermore, to overcome a problem with quantifying subjective utility function of ecological impacts, we measure them by so-called indicators of ecological stability. The resulting problem is stochastic programming problem formulated as (C)VaR model used traditionally in finance area. In our contribution we deal with convexity properties of this problem – these are especially important from the theoretical as well as from the computational point of view.
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On problem of optimization under incomplete information
Volf, Petr
The paper studies consequences of incomplete information to uncertainty of results of stochastic optimization. Stochastic characteristics of optimized system are evaluated from observed data, moreover, the data may be incomplete. Namely, we consider the random censoring of observations frequently encountered in time-to-event (of lifetime) studies. The analysis of uncertainty will be based both on theoretical properties of estimated stochastic characteristics and on simulated examples.
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Empirical Estimates in Economic and Financial Problems via Heavy Tails
Kaňková, Vlasta
Optimization problems depending on a probability measure correspond to many economic and financial applications. Complete knowledge of this measure is necessary to solve exactly these problems. Since this condition is fulfilled only seldom, the problem has to be usually solved on the data basis to obtain satistical estimates of an optimal value and optimal solutions. Great effort has been paid to investigate properties of these estimates; first under assumptions of disribution with thin tails and linear dependence on the probability measure. Recently, it has appeared an investigation in the case of nonlinear dependence on the probability measure and heavy tailed distributions with shape parameter greater two. We focus on the case of the stable and Pareto distributions with a shape parameter in the inteval (1, 2).
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Risk-Sensitive and Average Optimality in Markov Decision Processes
Sladký, Karel
This contribution is devoted to the risk-sensitive optimality criteria in finite state Markov Decision Processes. At first, we rederive necessary and sufficient conditions for average optimality of (classical) risk-neutral unichain models. This approach is then extended to the risk-sensitive case, i.e., when expectation of the stream of one-stage costs (or rewards) generated by a Markov chain is evaluated by an exponential utility function. We restrict ourselves on irreducible or unichain Markov models where risk-sensitive average optimality is independent of the starting state. As we show this problem is closely related to solution of (nonlinear) Poissonian equations and their connections with nonnegative matrices.
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