Stochastic Programming
Research in this field has more than
forty-year tradition in our department. Stochastic programming problems
are studied both theoretically and with respect to practical applications.
Presently, the group focuses on the following areas:
- Stability of
stochastic programming problems
- second-order
stochastic dominance constraints
- multi-objective
Problems
- dependent
probability constraints
- modelling
rational behavior on limit order markets
- mean-variance
optimality in markov decision processes
- growth rates
and average optimality in risk-sensitive markov decision
chains
- extended ramsey
growth model
- applications
in energy management
People
- Martin Branda
Stochastic optimization, transportation problems, integer programming
- Miloš Kopa
Stochastic dominance, option pricing
- Vlasta Kaňková
Stability, multiobjective problems, SSD constraints
- Karel Sladký
Dynamic programming, Markov decision chains
- Martin Šmíd
Approximation methods, applications to finance
- Michal Houda
Quantitative stability, probability constraints
- Vadym Omelchenko
Stochastic dynamic programming, applications in energy management
Selected publications
- Cavazos-Cadena R., Montes-de-Oca R.,
Sladký Karel :
A Counterexample on Sample-Path Optimality in Stable Markov Decision
Chains with the Average Reward Criterion, Journal of
Optimization Theory and Applications vol.163, 2 (2014), p. 674-684
- Dupačová, J., Kopa, M. (2014):
Robustness of optimal portfolios under risk and stochastic dominance
constraints, European Journal of Operational Research, 234, 2,
434-441.
- Branda Martin :
Stochastic programming problems with generalized integrated chance
constraints , Optimization vol.61, 8 (2012), p. 949-968
- Šmíd M. :
The Expected Loss in the Discretization of Multistage Stochastic
Programming Problems - Estimation and Convergence Rate, Annals
of Operations Research vol.165, 1 (2009), p. 29-45 (2009)
- Sladký K. :
Growth Rates and Average Optimality in Risk-Sensitive Markov
Decision Chains, Kybernetika vol.44, 2 (2008), p. 205-226 (2008)
- Kaňková V. : Multistage
Stochastic Programs via Autoregressive Sequences and Individual
Probabiliy Constraints , Kybernetika
vol.44, 2 (2008), p. 151-70 (2008)
- Kaňková V., Houda Michal : Depandent
samples in empirical estimation of stochastic programming problems
, Austrian Journal of Statistics vol.35, p. 271-279 (2006)
- van Dijk N. M., Sladký K.
: Monotonicity
and comparsion results for nonnegative dynamic system. Part I:
Discrete-time case , Kybernetika
vol.42, 1 (2006), p. 37-56 (2006)
- Sladký K., van Dijk N. M. : On
the Total Reward Variance for Continuous-Time Markov Reward Chains
, Journal of Applied Probability vol.43, 4 (2006), p. 1044-1052 (2006)
- Kaňková V., Šmíd Martin
: On
approximation in multistage stochastic programs: Markov dependence
, Kybernetika vol.40, 5 (2004), p. 625-638 (2004)
Grants and projects
- Stability analysis of optima and equilibria in economics
Martin Branda, grant No. 15-00735S of the
Czech Science Foundation.
- Arbitrage-free modelling of implied volatility in options
Miloš Kopa , grant No. GA13-25911S of the
Czech Science Foundation.
- New Trends in Stochastic Economic Models under Uncertainty
Vlasta Kaňková, grant No. 13-14445S of the
Czech Science Foundation.
- Stochastic Economic Models under Uncertainty: Development over
Time and Optimization
Vlasta Kaňková, grant No. P402/10/0956 of
the Czech Science Foundation.
- Rational Decision Making at Markets with Asynchronous Trading:
Theory and Empirical Evidence
Martin Šmíd, grant No. P402/10/1610
of the Czech Science Foundation
- Economic Decision Models: Dynamics and Risk
Karel Sladký, grant No.402/08/0107 of the
Czech Science Foundation, with Charles University of Prague.
- Economic Systems under Uncertainty: Optimization and
Approximation
Vlasta Kaňková, grant No. 402/07/1113 of
the Czech Science Foundation
- Mathematical modeling of the microstructure of the
financial markets with the non-synchronous trading
Martin Šmíd, grant
No.402/06/1417 of the Czech Science Foundation
- Validation of Economic Decision Models and Results
Karel Sladký, grant No.402/05/0115 of the
Czech Science Foundation, with Charles University of Prague.
- Stochastic Decision Approaches in Nonlinear Economic Models
Vlasta Kaňková, grant No. 402/04/1294 of
the Czech Science Foundation.