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Iмовiрнiсний огляд ймовiрностей дефолту для портфелiв з низьким рiвнем дефолту введених К. Плуто та Д. Таше
Full text linkThis article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of default is involved under the influence of systematic factor. The author anticipates adding more clarity, especially for early career analysts or scholars, regarding the assumption of borrowers\u27 independence, conditional independence, and interaction between the probability distributions such as binomial, beta, normal, and others. There is also shown the relation between the probability of default and the joint distribution of \sqrt{ϱ}X - \sqrt{1-ϱ}Y, where X, including but not limiting, is the standard normal, Y admits, including but not limiting, the beta-normal distribution and X, Y are independent.
Pages of the article in the issue: 63 - 74
Language of the article: EnglishУ цiй статтi подано огляд методу, що широко використовується для оцiнювання ймовiрностi дефолту, запропонований К. Плутоном i Д. Таше. Наведено припущення та отримано нерiвнiсть, в якiй ймовiрнiсть дефолту залежить вiд впливу систематичного фактору
Problem of maximal profit-risk ratio.
No full textThe main subject of the final Bachelor thesis is the investment portfolio optimization problem, which has the objective to maximise profit-risk ratio by using a methods of the linear algebra and Harry Markowitz modern portfolio theory. By the time world is noticeably modernizing and the global economy prospers rapidly, the size of investment flows and financial budgets is constantly increasing, and this leads to an increased importance level of investment in the daily world. Both management and investment of the budget consist of the multitude different factors, therefore the modern portfolio theory was introduced to the world with the primary aim of optimizing the investment portfolio by the United States Economist Harry Markowitz. Another extremely important person in a development of the problem of portfolio optimization problem is the US economist William F. Sharpe, who found a way how to optimize the investment portfolio by maximizing the relationship between portfolio return and risk and this profit-risk coefficient is called Sharpe ratio. The theoretical part of the thesis provides an overview of the mathematical factors that influence the portfolio optimization problem. The statements of modern portfolio theory will also be introduced which along with the methods of the linear algebra will help to formulate the maximization problem of the profit-risk ratio. In the practical part of the thesis I will motivate the statements provided in the theoretical part and using the historical stock exchange data of the three Baltic companies, I will form the investment portfolio by three risky assets and after all I will optimize the investment portfolio by finding the maximum value of profit-risk ratio
Investment portfolio optimization.
No full textInvestment Portfolio Optimization This work analyses optimization of an investment portfolio, which consists of n risky assets, and the optimization of n risky assets plus one risk-free, which is fixed return asset. Work briefly introduces the theory of investment, Markowitz and Sharpe's works, proves Sharpe ratio and mean variance statements, and using proven statements forms portfolios that consists of real historical data and briefly compares formed portfolios
Stock portfolio optimization based on modern potfolio theory.
No full textThis thesis represents H. Markowitz Theory and its main concepts. Thesis consists of two parts: theoretical and practical application. In the first part main aspects of portfolio optimization and methods of calculating indicators are explained. Three optimal portfolios are formed in the second part - minimum risk portfolio, maximum return for a given level of risk portfolio and maximum Sharpe ratio portfolio. The aim of this article is to show how H. Markowitz theory based portfolio optimization can be applied to 10 largest stocks traded on Vilnius Nasdaq stock Exchange
Probability of default modeling under the effect of systematic factor.
No full textThis Bachelor’s thesis analyses one of the credit risk components’ - probability of default. The case, when events of default are independent of each other but are under the effect of the same systematic factor - asset correlation, was chosen. The purpose of this thesis is to analyse the structure of inequality which is used to find probability of default using most prudent estimation principle. According to the found formulas, certain examples of probabilities of defaults were modeled
Survival probability generating functions of bi-seasonal discrete time risk model.
No full textIn this bachelor thesis we investigate the discrete time risk model when premium rate equals one or two. Here claims are interchangeably occurring independent but not necessarily identically distributed. We try to find probability generating functions that best fit models described bellow in order to find ultimate time survival probability for bi-seasonal discrete time risk model when premium rate equals two or one
Ruin probabilities of a discrete-time bi-seasonal model.
No full textThis bachelor thesis is related with ruin probability of seasonal discrete time risk model. In this case, we choose model of two different claims where one claim happens in odd and another in even time units. According to it, occured claims reduce insurer's surplus. Therefore, we submit recursive formula to calculate ruin probability in bi-seasonal discrete time risk model and its proof. Consequently, theoretical part is illustrated with numerical examples
Passive investment strategy-based portfolio formation and optimization.
No full textThis thesis approaches optimization of passive investment strategy-based portfolios. Works consists of 2 parts: theoreticat part that covers H. Markowitz modern portfolio theory and optimization, practical analysis part that covers portfolio optimization use on passive investment strategy-based portfolio and test multiple optimized portfolios including Ray Dalio’s "All Seasons Portolfio"
Investment portfolio optimization.
No full textIn this bachelor's work there is determined the investment portfolio and the main portfolio parameters, such as the standard deviation (risk level) and investment return. Based on H. Markowitz’s modern portfolio theories, these parameters are evaluated and calculated for the formation of portfolio efficient frontier. The portfolio is optimized in two ways - by setting specific investment returns and minimizing risk, or by fixing a certain level of risk and maximizing the return of the established risk limits. The optimization is adapted to a minimum portfolio which is consisted of two investment instruments and also a portfolio consisting of infinity investment instruments. The results obtained will be validated with portfolio data selected from the Nasdaq corporate databases
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