|
|
Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees can be also combined with Markov chains which describe the state of the system and determine which scenario tree should be used. Another structure which enables reduce the complexity of the problem is a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used for representation of random returns as the input to the investment problem.
|
|
|
Stochastic Programming Problems in Asset-Liability Management
Rusý, Tomáš ; Kopa, Miloš (advisor)
The main objective of this thesis is to build a multi-stage stochastic pro- gram within an asset-liability management problem of a leasing company. At the beginning, the business model of such a company is introduced and the stochastic programming formulation is derived. Thereafter, three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint are applied to the model to control for riski- ness of the optimal strategy. Their properties and their effects on the optimal decisions are thoroughly investigated, while various risk limits are considered. In order to obtain solutions of the problems, random elements in the model formulation had to be approximated by scenarios. The Hull - White model calibrated by a newly proposed method based on maximum likelihood esti- mation has been used to generate scenarios of future interest rates. In the end, the performances of the optimal solutions of the problems for unconsid- ered and unfavourable crisis scenarios were inspected. The used methodology of such a stress test has not yet been implemented in stochastic programming problems within an asset-liability management. 1
|
|
|
Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees combined with Markov chains are also introduced. Markov chains states determine if there is a crisis period or not. Information about historical number of crises helps us to construct a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used as an input to the investment problem.
|
|
|
Stochastic Programming Problems in Asset-Liability Management
Rusý, Tomáš ; Kopa, Miloš (advisor)
The main objective of this thesis is to build a multi-stage stochastic pro- gram within an asset-liability management problem of a leasing company. At the beginning, the business model of such a company is introduced and the stochastic programming formulation is derived. Thereafter, three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint are applied to the model to control for riski- ness of the optimal strategy. Their properties and their effects on the optimal decisions are thoroughly investigated, while various risk limits are considered. In order to obtain solutions of the problems, random elements in the model formulation had to be approximated by scenarios. The Hull - White model calibrated by a newly proposed method based on maximum likelihood esti- mation has been used to generate scenarios of future interest rates. In the end, the performances of the optimal solutions of the problems for unconsid- ered and unfavourable crisis scenarios were inspected. The used methodology of such a stress test has not yet been implemented in stochastic programming problems within an asset-liability management. 1
|
|
|
Scenario structures in multistage stochastic programs
Harcek, Milan ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multi-stage stochastic programming in the context of random process representation. Basic structure for random process is a scenario tree. The thesis introduces general and stage-independent scenario tree and their properties. Scenario trees can be also combined with Markov chains which describe the state of the system and determine which scenario tree should be used. Another structure which enables reduce the complexity of the problem is a scenario lattice. Scenario generation is performed using moment method. Scenario trees are used for representation of random returns as the input to the investment problem.
|
|
|
Stochastic Programming Problems in Asset-Liability Management
Rusý, Tomáš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
The main objective of this thesis is to build a multi-stage stochastic pro- gram within an asset-liability management problem of a leasing company. At the beginning, the business model of such a company is introduced and the stochastic programming formulation is derived. Thereafter, three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint are applied to the model to control for riski- ness of the optimal strategy. Their properties and their effects on the optimal decisions are thoroughly investigated, while various risk limits are considered. In order to obtain solutions of the problems, random elements in the model formulation had to be approximated by scenarios. The Hull - White model calibrated by a newly proposed method based on maximum likelihood esti- mation has been used to generate scenarios of future interest rates. In the end, the performances of the optimal solutions of the problems for unconsid- ered and unfavourable crisis scenarios were inspected. The used methodology of such a stress test has not yet been implemented in stochastic programming problems within an asset-liability management. 1
|
|
|
Multistage Stochastic Programming Problems - Decomposition
Lapšanská, Alica ; Kaňková, Vlasta (advisor) ; Lachout, Petr (referee)
The thesis deals with a multistage stochastic model and its application to a number of practical problems. Special attention is devoted to the case where a random element follows an autoregressive sequence and the constraint sets correspond to the individual probability constraints. For this case conditions under which is the problem well-defined are specified. Further, the approximation of the problem and its convergence rate under the empirical estimate of the distribution function is analyzed. Finally, an example of the investment in financial instruments is solved, which is defined as a two-stage stochastic programming problem with the probability constraint and a random element following an autoregressive sequence. Powered by TCPDF (www.tcpdf.org)
|
|
|
Multi-Stage Stochastic Programming with CVaR: Modeling, Algorithms and Robustness
Kozmík, Václav ; Dupačová, Jitka (advisor) ; Morton, David (referee) ; Kaňková, Vlasta (referee)
Multi-Stage Stochastic Programming with CVaR: Modeling, Algorithms and Robustness RNDr. Václav Kozmík Abstract: We formulate a multi-stage stochastic linear program with three different risk measures based on CVaR and discuss their properties, such as time consistency. The stochastic dual dynamic programming algorithm is described and its draw- backs in the risk-averse setting are demonstrated. We present a new approach to evaluating policies in multi-stage risk-averse programs, which aims to elimi- nate the biggest drawback - lack of a reasonable upper bound estimator. Our approach is based on an importance sampling scheme, which is thoroughly ana- lyzed. A general variance reduction scheme for mean-risk sampling with CVaR is provided. In order to evaluate robustness of the presented models we extend con- tamination technique to the case of large-scale programs, where a precise solution cannot be obtained. Our computational results are based on a simple multi-stage asset allocation model and confirm usefulness of the presented procedures, as well as give additional insights into the behavior of more complex models. Keywords: Multi-stage stochastic programming, stochastic dual dynamic programming, im- portance sampling, contamination, CVaR
|
guest ::
