National Repository of Grey Literature 26 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Log-optimal investment
Král, Stanislav ; Dostál, Petr (advisor) ; Večeř, Jan (referee)
1. Abstrakt Suppose we have a capital, which we will redistribute into investment op- portunities. The financial valuation of these investments will be a sequence of independent, identically distributed random vectors that acquire finite amount of values. We will have full knowledge of the entire history of these valuations before each investment. It turns out that if our strategy is to always maximizes the mean value of the logarithm of the investment value, denoted by Λ∗ , then this strategy is asymptotically the best one possible. If strategy Λ is not asymptotically close to Λ∗ and if x goes to infinity, then the mean of the time we earn atleast x using Λ∗ is infinitely smaller than the time if we used Λ. We also earn infinitely times more money using the strategy Λ∗ . 1
Maximum Return Portfolio
Palko, Maximilián ; Večeř, Jan (advisor) ; Šmíd, Martin (referee)
Classical method of portfolio selection is based on minimizing the variabi- lity of the portfolio. The Law of Large Numbers tells us that in case of longer investment horizon it should be enough to invest in the asset with the highest expected return which will eventually outperform any other portfolio. In our thesis we will suggest some portfolio creation methods which will create Maxi- mum Return Portfolios. These methods will be based on finding the asset with maximal expected return. That way we will avoid the problem of estimation errors of expected returns. Two of those methods will be selected based on the results of simulation analysis. Those two methods will be tested with the real stock data and compared with the S&P 500 index. Results of the testing suggest that our portfolios could have an application in the real world. Mainly because our portfolios showed to be significantly better than the index in the case of 10 year investment horizon. 1
The Stigler-Luckock model for a limit order book
Fornůsková, Monika ; Swart, Jan (advisor) ; Večeř, Jan (referee)
THE STIGLER-LUCKOCK MODEL FOR A LIMIT ORDER BOOK Abstract One of the types of modern-day markets are so-called order-driven markets whose core component is a database of all incoming buy and sell orders (order book). The main goal of this thesis is to extend the Stigler-Luckock model for order books to give a better insight into the price forming process and behaviour of the market participants themselves. The model introduced in this thesis focuses on a comparison of behaviour and various strategies of market makers who are sophisticated market participants profiting from extensive trading. The market is described using Markov chains, and the strategies are compared using Monte Carlo simulations and game theory. The results showed that market makers' orders should have small spread and large volumes. The final model compares two strategies in which market makers monitor their portfolio. In case of having more cash than asset (or vice versa), they shift prices of their orders to equalise the portfolio. The model recommends checking the market quite often, but acting conservatively, which means not changing prices that frequently and not jumping to conclusions just from a small imbalance in the portfolio.
Statistical machine learning with applications in music
Janásková, Eliška ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of this thesis is to review the current state of machine learning in music composition and to train a computer on Beatles' songs using research project Magenta from the Google Brain Team to produce its own music. In order to explore the qualities of the generated music more thoroughly, we restrict our- selves to monophonic melodies only. We train three deep learning models with three different configurations (Basic, Lookback, and Attention) and compare generated results. Even though the generated music is not as interesting as the original Beatles, it is quite likable. According to our analysis based on musically informed metrics, generated melodies differ from the original ones especially in lengths of notes and in pitch differences between consecutive notes. Generated melodies tend to use shorter notes and higher pitch differences. In theoretical background, we cover the most commonly used machine learning algorithms, introduce neural networks and review related work of music generation. 1
Parameter choice in portfolio optimization problems based on out-of-sample performance
Vaňková, Kateřina ; Kopa, Miloš (advisor) ; Večeř, Jan (referee)
This thesis investigates three optimization models using the rolling window method. These models are based on maximizing profits and minimizing risk. Two statistics are considered in the models: expected value and a risk measure. Risk measures analyzed in this thesis are: the variance, the Conditional Value-at-Risk at a specified confidence level, and the Mean Absolute Deviation. Models are tested on the real US stock data of ten companies in the time period of twenty years: from January 30th, 1999 to January 30th, 2019. The aim of this thesis is to analyze these models using the rolling window method and to investigate its sensitivity towards changes in the values of several parameters in order to identify the best parameter setting.
Volatility modeling
Jurka, Vojtěch ; Prášková, Zuzana (advisor) ; Večeř, Jan (referee)
In the thesis we deal with modelling volatility conditional on past shocks. Traditional ARCH and GARCH models proposed by Engle(1982) and Bollerslev(1986) are investigated as well as several generalizations of GARCH model that capture asymmetric reaction on positive and negative excess returns, namely GJR-GARCH, TGARCH and EGARCH. Selected models are then applied to four commodities traded on Chicago Mercantile Exchange that represent various sectors of commodity market. Our first key finding is that in short horizon all considered models have similar performance, while in longer horizon, EGARCH and TGARCH give more precise results. The second is that, measured by an average percentage error, there is no significant difference in quality of predictions among selected assets across commodity sectors.
Reverse mortgage
Korotkov, Daniil ; Mazurová, Lucie (advisor) ; Večeř, Jan (referee)
ČSOB Pojišťovna, a. s., člen holdingu ČSOB Veřejné 1 / 1 20.7.2018 Abstract: At this moment, reverse mortgages are relatively new products on the Czech market and this thesis deals with their problematics. In this thesis, we describe the main risks related to reverse mortgages, namely, longevity risk and adverse evolution of property prices. Analyzing these risks we are modelling the underlying property prices, their future behavior, discount factors along with studying the risk models such as vector autoregression, hedonic model, repeat-sales and Wills-Sherris model. In practical part, we focus on estimating the parameters of Lee-Carter model and autoregression model of zero-coupon government bond as well as applying the results of the estimation to calculate various characteristics of reverse mortgages.
Market model with random inputs
Krch, Ivan ; Lachout, Petr (advisor) ; Večeř, Jan (referee)
The thesis deals with market models with random inputs represented by the newsvendor problem for which the randomness is given through a random number of customers. Presented work is divided into three chapters. In the first chapter we present the elementar newsvendor problem as stochastic programming problem with a fixed recourse. In the second chapter we present the multiplayer game theory adapted to the newsvendors problem. Moreover, in the second chapter we extend the problem by the second newsvendor on the market and in the third chapter we generalize the problem for n newsvendors on the market. We deal with the situations that arise in the chapters two and three from the game theory point of view and we study characteristics of a Nash equilibrium. Presented theory is demonstrated on illustrative examples in the ends of the two last chapters. 1
Optimal portfolios
Vacek, Lukáš ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
In this diploma thesis, selected techniques for construction of optimal portfo- lios are presented. Risk measures and other criteria (Markowitz approach, Value at risk, Conditional value at risk, Mean absolute deviation, Spectral risk measure and Kelly criterion) are defined in the first part. We derived analytical solution for some cases of optimization problems, in some other cases there exists numeri- cal solution only however. Advantages and disadvantages, theoretical properties and practical aspects of software implementation in Wolfram Mathematica are also mentioned. Simulation methods suitable for portfolio optimization are brie- fly presented with their motivation in the second part. Multivariate distributions: normal, t-distribution and skewed t-distribution are presented in the third part with connection to optimization of portfolio with assumption of multivariate dis- tribution of financial losses. Optimization methods are illustrated on real data in the fourth part of this thesis. Analytical methods are compared with numerical ones. 1
Machine learning with applications to finance
Mešša, Samuel ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
The impact of data driven, machine learning technologies across a wide variety of fields is undeniable. The financial industry, which relies heavily on predictive modeling being no exception. In this work we summarize two widely used machine learning models: support vector machines and neural networks, discuss their limitations and compare their performance to a more traditionally used method, namely logistic regression. Evaluation was done on two real world datasets, which were used to predict default of loan applicants and credit card holders formulated as a binary classification task. Neural networks and support vector machines either outperformed or showed comparable results to logistic regression with performance measured in receiver operator characteristic area under curve. In the second task neural networks outperformed both other models by a significant margin.

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