
MultiObjective Optimization Problems with Random Elements  Survey of Approaches
Kaňková, Vlasta
Many economic and financial situations depend simultaneously on a random element and a decision parameter. Mostly, it is possible to influence the above mentioned situation only by an optimization model depending on a probability measure. This optimization problem can be static (onestage), dynamic with finite or infinite horizon, singleobjective or multiobjective. We focus on onestage multiobjective problems corresponding to applications those are suitable to evaluate simultaneously by a few objectives. The aim of the contribution is to give a survey of different approaches (as they are known from the literature) of the above mentioned applications. To this end we start with wellknown meanrisk model and continue with other known approaches. Moreover, we try to complete every model by a suitable application. Except an analysis of a choice of the objective functions type we try to discuss suitable constraints set with respect to the problem base, possible investigation and relaxation. At the end we mention properties of the problem in the case when the theoretical „underlying“ probability measure is replaced by its „deterministic“ or „stochastic“ estimate.


Risksensitive and Mean Variance Optimality in Continuoustime Markov Decision Chains
Sladký, Karel
In this note we consider continuoustime Markov decision processes with finite state and actions spaces where the stream of rewards generated by the Markov processes is evaluated by an exponential utility function with a given risk sensitivitycoefficient (socalled risksensitive models). If the risk sensitivity coefficient equals zero (riskneutral case) we arrive at a standard Markov decision process. Then we can easily obtain necessary and sufficient mean reward optimality conditions and the variability can be evaluated by the mean variance of total expected rewards. For the risksensitive case, i.e. if the risksensitivity coefficient is nonzero, for a given value of the risksensitivity coefficient we establish necessary and sufficient optimality conditions for maximal (or minimal) growth rate of expectation of the exponential utility function, along with mean value of the corresponding certainty equivalent. Recall that in this case along with the total reward also its higher moments are taken into account.


Problem of competing risks with covariates: Application to an unemployment study
Volf, Petr
The study deals with the methods of statistical analysis in the situation of competing risks in the presence of regression. First, the problem of identification of marginal and joint distributions of competing random variables is recalled. The main objective is then to demonstrate that the parameters and, in particular, the correlation of competing variables, may depend on covariates. The approach is applied to solution of a real example with unemployment data. The model uses the Gauss copula and Cox’s regression model.


Two Algorithms for Riskaverse Reformulation of Multistage Stochastic Programming Problems
Šmíd, Martin ; Kozmík, Václav
Many reallife applications lead to riskaverse multistage stochastic problems, therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, CoinOR, APML or, for smaller problems, Excel), it is, however, mostly up to researcher to reformulate the problem into its deterministic equivalent. Moreover, such solutions are usually onetime, not easy to modify for different applications. We overcome these problems by providing a frontend software package, written in C++, which enables to enter problem definitions in a way close to their mathematical definition. Creating of a deterministic equivalent (and its solution) is up to the computer. In particular, our code is able to solve linear multistage with Multiperiod MeanCVaR or Nested MeanCVaR criteria. In the present paper, we describe the algorithms, transforming these problems into their deterministic equivalents.
