Stochastic optimization

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.