National Repository of Grey Literature 158 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Optimization of Value at Risk using integer programming
Fausek, Matěj ; Branda, Martin (advisor) ; Procházka, Vít (referee)
This thesis is focused on the portfolio optimization problem. The foundations of this problem were laid by Professor Markowitz (1952), who measured risk using the standard deviation of random returns. In this paper, the standard deviation will be replaced by the Value at Risk function. We will show that if the number of past observations or the number of assets is limited by a constant, there will be an algorithm that can solve the problem in a reasonable amount of time. We will formulate the problem as a mixed-integer linear optimization problem. This paper also includes computation on real data. 27
Forecasting age distribution of death counts with applications in life insurance pricing
Škopek, Pavel ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
This thesis deals with the topic of mortality modelling and life insurance pricing. First, basic concepts from the demographic model and life tables are introduced. Following is a description of the Lee-Carter model including three methods for estimating of parameters and predicting of future values. The the- sis also analyses the Renshaw-Haberman model and the method, which uses compositional data analysis including the non-parametric bootstrap for interval estimations. Besides the theoretical part the thesis also contains a practical one, where Czech mortality data are modeled separately for men and women. Based on the data from 1970-2021 we select the best model, predict future values for 30 years ahead and price the life insurance in 2021 and in the following years. 1
Optimalizace plánování tras a rozvrhů svozu odpadu
Loub, Pavel ; Procházka, Vít (advisor) ; Branda, Martin (referee)
This thesis proposes a mixed integer linear program for waste collection in South Moravian region. For deterministic models are difficult to solve by exact methods, it was necessary to find a way to obtain solutions in reasonable time. Hence, a brand new metaheuristic based on Simulated annealing is developed for solving the waste collection problem. 1
Index tracking problem using risk measures
Polakovičová, Andrea ; Branda, Martin (advisor) ; Šmíd, Martin (referee)
In this thesis, we will introduce various methods for measuring risk known as Value at Risk (V aR) and Conditional Value at Risk (CV aR). We will use their properties and formulations in deriving a linear optimization problem. The linear programming problem will consist of minimizing the objective function representing the deviation between the portfolio and a chosen index. The calculation will be carried out based on multiple constraints, where one of them will use the aforementioned risk measures V aR and CV aR. The goal is to create a portfolio based on this program that replicates the S&P 500 index. We will perform the entire calculation using Python based on historical data. Subsequently, we will use the optimal solution found by the software and construct a replication portfolio that we will track in the following time periods. In conclusion, we will analyze and discuss the individual results for various input parameters. 1
Optimal choice of scenario tree using Reinforcement learning
Vondráček, Jakub ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
This thesis deals with multistage stochastic programs and explores the dependence of the obtained objective value on the chosen structure of the scenario tree. In particular, the scenario trees are built using the moment matching method, a multistage mean-CVaR model is formulated and a reinforcement learning agent is trained on a set of historical financial data to choose the best scenario tree structure for the mean-CVaR model. For this purpose, we implemented a custom reinforcement learning environment. Further an inclusion of a penalty term in the reward obtained by the agent is proposed to avoid scenario trees that are too complex. The reinforcement learning agent is then evaluated against an agent that chooses the scenario tree structure at random and outperforms the random agent. Further the structure of scenario trees chosen by the reinforcement learning agent is analyzed. 1
Scheduling problems under uncertainty with nonidentical machines
Matoušková, Monika ; Branda, Martin (advisor) ; Lachout, Petr (referee)
This thesis deals with operational fixed interval scheduling problems under uncer- tainty. The topic has been covered for identical machines and the theory is summarized in this thesis. The stochastic programming problem has a deterministic reformulation based on network flow under the assumption that the multivariate distribution of ran- dom delays follows an Archimedean copula. In this thesis, we focus on the problem with heterogeneous machines. When there are more possible types of machines, this problem somewhat complicates. The deterministic problem with no delays and more than one machine type is NP-hard. We generalized the deterministic reformulation of the stochas- tic problem with possible random delays for nonidentical machines. This formulation for more than one machine type loses an important property that holds for identical machines reformulation using network flow. Then an algorithm based on Lagrangean relaxation is proposed, implemented and compared with a solution obtained by MIP solver. 1
Sparsity and regularization in portfolio selection problems
Kaľatová, Monika ; Branda, Martin (advisor) ; Šmíd, Martin (referee)
This thesis focuses on a problem which decision vector has limited number of non- zero elements. This limitation is ensured by adding cardinality constraint, but solving the mixed-integer reformulation of the problem is difficult. This mixed-integer problem is relaxed and then regularized or the exact penalty function is added. These two apporaches are described and applied on the portfolio theory. For this special type of problems we show relations between these two approaches. Basic summary of the theory of risk measures is used in numerical study, in which we compare penalization functions for few types of problems. 1
Convergence of stochastic gradient descent in machine learning problems
Jelínková, Marie ; Branda, Martin (advisor) ; Kozmík, Karel (referee)
The aim of this thesis is solving minimization problems where the objective function is a sum of a differentiable (yet possibly non-convex) and general convex function. We focus on methods of stochastic and projected gradient descent from machine learning. By combining those two approaches we introduce an algorithm for solving such problems. The work is composed in a gradual manner where we firstly define necessary concepts needed for describing RSPG algorithm. Then we proceed to show the convergence of the algorithm for both convex and non-convex objective functions. A short numerical study is also included at the end. 1
Sparse solutions in labeling optimization problems
Komora, Ondřej ; Branda, Martin (advisor) ; Lachout, Petr (referee)
The main goal of this work is to give self-contained description of proximal and ordi- nary stochastic subgradient descent methods, which are used in finding sparse solutions of labeling optimization problems. We will define and interpret necessary concepts lea- ding to the definition of those methods and we will discuss in detail conditions, under which we show convergence of these methods to critical point. At the end, we will pre- sent a numerical experiment on concrete optimization task where we demonstrate use of these methods. In this experiment we will also show how a suitable choice of so called regularization can influence sparsity of solution of this particular task. 1
Asset-Liability Management:Application of Stochastic Programmingwith Endogenous Randomness andContamination
Rusý, Tomáš ; Kopa, Miloš (advisor) ; Consigli, Giorgio (referee) ; Branda, Martin (referee)
Title: Asset-Liability Management: Application of Stochastic Programming with Endogenous Randomness and Contamination Author: RNDr. Tomáš Rusý Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, PhD., Department of Probability and Mathematical Statistics Abstract: This thesis discusses a stochastic programming asset-liability management model that deals with decision-dependent randomness and a subsequent contamination analysis. The main model focuses on a pricing problem and the connected asset- liability management problem describing the typical life of a consumer loan. The endogeneity stems from the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepay- ment which are all affected by the company's decision on interest rate of the loan. Another important factor, which plays a major role for liabilities, is the price of money in the market. There, we focus on the scenario generation procedure and develop a new calibration method for estimating the Hull-White model [Hull and White, 1990] under the real-world measure. We define the method for the gen- eral class of one-factor short-rate models and perform an extensive analysis to assess the estimation performance and...

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