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Reinsurance optimization using stochastic programming and risk measures
Došel, Jan ; Branda, Martin (advisor) ; Cipra, Tomáš (referee)
Title: Reinsurance optimization using stochastic programming and risk measures Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Martin Branda, Ph.D., Department of Probability and Mathe- matical Statistics Abstract: The diploma thesis deals with an application of a stochastic progra- mming in a reinsurance optimization problem in terms of a present regulatory framework of the insurance companies within the European Union, i.e. Solvency II. In this context, the reinsurance does not only transfer a portion of the risk to the reinsurer but also reduces an amout of required capital. The thesis utilizes certain risk measures and their properties, premium principles and non-linear in- teger programming. In the theoretical part, there are basic terms from Solvency II, reinsurance, risk measures and the comonotonicity of random variables descri- bed and the optimization problem itself is derived. The approach is then applied in the practical part on data of Czech Insurers' Bureau using the GAMS software. Finally, a stability of the solution is tested depending on several parameters. Keywords: reinsurance optimization, stochastic programming, Solvency II, risk measures 1
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Means testing with an application to economic data
Došel, Jan ; Zichová, Jitka (advisor) ; Hlávka, Zdeněk (referee)
Title: Means testing with an application to economic data Author: Jan Došel Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The bachelor thesis deals with multivariate analysis of variance as a sta- tistical tool for comparing means of several random samples. In theoretical part, basic terms are described. Furthermore, a test statistic is derived from likelihood functions. The method is demonstrated by a simulation study in practical part. Keywords: analysis of variance, hypothesis testing, multivariate normal distribu- tion, likelihood function 1
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