<p>Radiation quality is described by the RBE (relative biological effectiveness) that varies with the ionizing ability of the radiation. Microdosimetric quantities describe distributions of energy imparted to small volumes and can be related to RBE. This has made microdosimetry a powerful tool for radiation quality determinations in both radiation protection and radiation therapy. The variance-covariance method determines the dose-average of the distributions and has traditionally been used with two detectors to correct for beam intensity variations. Methods to separate dose components in mixed radiation fields and to correct for beam variations using only one detector have been developed in this thesis. Quality factor relations have been optimized for different neutron energies, and a new algorithm that takes single energy deposition events from densely ionizing radiation into account has been formulated. The variance-covariance technique and the new methodology have been shown to work well in the cosmic radiation field onboard aircraft, in the mixed photon and neutron fields in the nuclear industry and in pulsed fields around accelerators.</p><p>The method has also been used for radiation quality characterization in therapy beams. The biological damage is related to track-structure and ionization clusters and requires descriptions of the energy depositions in nanometre sized volumes. It was shown that both measurements and Monte Carlo simulation (condensed history and track-structure) are needed for a reliable nanodosimetric beam characterization. The combined experimental and simulated results indicate that the dose-mean of the energy imparted to an object in the nanometre region is related to the clinical RBE in neutron, proton and photon beams. The results suggest that the variance-covariance technique and the dose-average of the microdosimetric quantities could be well suited for describing radiation quality also in therapy beams.</p>

Radiation quality is described by the RBE (relative biological effectiveness) that varies with the ionizing ability of the radiation. Microdosimetric quantities describe distributions of energy imparted to small volumes and can be related to RBE. This has made microdosimetry a powerful tool for radiation quality determinations in both radiation protection and radiation therapy. The variance-covariance method determines the dose-average of the distributions and has traditionally been used with two detectors to correct for beam intensity variations. Methods to separate dose components in mixed radiation fields and to correct for beam variations using only one detector have been developed in this thesis. Quality factor relations have been optimized for different neutron energies, and a new algorithm that takes single energy deposition events from densely ionizing radiation into account has been formulated. The variance-covariance technique and the new methodology have been shown to work well in the cosmic radiation field onboard aircraft, in the mixed photon and neutron fields in the nuclear industry and in pulsed fields around accelerators. The method has also been used for radiation quality characterization in therapy beams. The biological damage is related to track-structure and ionization clusters and requires descriptions of the energy depositions in nanometre sized volumes. It was shown that both measurements and Monte Carlo simulation (condensed history and track-structure) are needed for a reliable nanodosimetric beam characterization. The combined experimental and simulated results indicate that the dose-mean of the energy imparted to an object in the nanometre region is related to the clinical RBE in neutron, proton and photon beams. The results suggest that the variance-covariance technique and the dose-average of the microdosimetric quantities could be well suited for describing radiation quality also in therapy beams.

This thesis is focused on a theoretical explication of the basic methods of the calculation Value at Risk for the market and credit risk. For the market risk there is in detail developed the variance -- covariance method, historical simulation and Monte Carlo simulation, above all for the nonlinear portfolio. For all methods the assumptions of their applications are highlighted and the comparation of these methods is made too. For the credit risk there is made a theoretical description of CreditMetrics, CreditRisk+ and KMV models. Analytical part is concerned in the quantification of Value at Risk on two portfolios, namely nonlinear currency portfolio, which particular assumptions of the variance -- covariance method a Monte Carlo simulation are tested on. Then by these methods the calculation of Value at Risk is realized. The calculation of Credit Value at Risk is made on the portfolio of the US corporate bonds by the help of CreditMetrics model.

The diploma thesis "Value at Risk: Historical simulation, variance covariance method and Monte Carlo" aims to value the risk which real bond portfolio bears. The thesis is decomposed into two major chapters: Theoretical and Practical chapters. The first one speaks about VaR and conditional VaR theory including their advantages and disadvantages. Moreover, there are described three basic methods to calculate VaR and CVaR with adjustments to each method in order to increase the reliability of results. The last chapter brings results of VaR and CVaR computation. Many graphs, tables and images are added to the result section in order to make the outputs more visible and well-arranged.

The goal of the paper is to compare impacts of interest rate risk measuring meth-ods on capital requirements. The first section identifies methods for measuring interest rate risk and capital requirements for interest rate risk set by regulators. The second section compares capital requirements of model portfolio calculated by using standardized methods as well as internal models.

Magistro darbe nagrinėjamas šiuo metu vienas moderniausių rizikos matų – rizikos vertė (angl.Value-at-risk) Analizuojami trys pagrindiniai VaR rodiklio skaičiavimo metodai: variacijos/kovariacijos, istorinio modeliavimo ir Monte Karlo simuliacijos keliamų prielaidų, sudėtingumo ir adekvatumo požiūriais. Visų trijų metodų pagalba dabartinėmis rinkos sąlygomis atliekami empiriniai tyrimai, siekiant įvertinti rizikos vertes valiutų ir akcijų rinkose, atlikta gautų rizikos verčių palyginamoji analizė bei patikrintas naudotų metodų tikslumas. Autorės suformuluota hipotezė, kad VaR rodiklio skaičiavimo metodai nėra tinkami naudoti pereinamuoju laikotarpiu kuomet ekonominė aplinka ir padėtis nėra stabili iš dalies patvirtinta, nes atliktų tyrimų rezultatai atmetė tik variacijos/kovariacijos bei istorinio modeliavimo metodų tinkamumą. / In this master‘s work analyzed one of the modern risk measurements – Value-at-Risk (VaR). The paper examined three main VaR calculation methods: variance/covariance, historical simulation and Monte Carlo generations satisfying in the terms of the assumptions, adequacy and complexity. For all three methods was carried out empirical studies to assess the risk of currency and stock markets, made comparative analysis of the obtained risk values and verified accuracy of used methods in the current market conditions. The authors formulated the hypothesis that the VaR indicator calculation methods are not suitable for use during the transitional period when the economic environment and situation is not stable partially confirmed because the results of tests performed to reject just the variance / covariance and historical simulation methods.

Diploma thesis Business risks in insurance and their quantification describes the business risks to which insurance companies are exposed in their activities. Thesis is focused on market risk and quantification of market risk in insurance companies. It includes determination of the specifications for the activities of insurance companies, regulation and characteric of business risks in insurance. Large part of the thesis deals with the method of Value at Risk as a tool to measure market risk as well as individual methods to calculate it. In the conclusion, thesis describes the processes of quantification of market risk in Generali PPF Holding and in Česká poisťovňa, which gives a practical insight into the issues of market risk in insurance companies.

風險值大多是在假設資產報酬為常態分配下計算而得的，但是這個假設與實際的資產報酬分配不一致，因為很多研究者都發現實際的資產報酬分配都有厚尾的現象，也就是極端事件的發生機率遠比常態假設要來的高，因此利用常態假設來計算風險值對於真實損失的衡量不是很恰當。 針對這個問題，本論文以歷史模擬法、變異數-共變異數法、混合常態模型來模擬報酬率的分配，並依給定的信賴水準估算出風險值，其中混合常態模型的參數是利用準貝式最大概似估計法及EM演算法來估計；然後利用三種風險值的評量方法：回溯測試、前向測試與二項檢定，來評判三種估算風險值方法的優劣。 經由實證結果發現： 1.報酬率分配在左尾臨界機率1％有較明顯厚尾的現象。 2.利用混合常態分配來模擬報酬率分配會比另外兩種方法更能準確的捕捉到左尾臨界機率1％的厚尾。 3.混合常態模型的峰態係數值接近於真實報酬率分配的峰態係數值，因此我們可以確認混合常態模型可以捕捉高峰的現象。 關鍵字：風險值、厚尾、歷史模擬法、變異數-共變異教法、混合常態模型、準貝式最大概似估計法、EM演算法、回溯測試、前向測試、高峰 / Initially, Value at Risk (VaR) is calculated by assuming that the underline asset return is normal distribution, but this assumption sometimes does not consist with the actual distribution of asset return. Many researchers have found that the actual distribution of the underline asset return have Fat-Tail, extreme value events, character. So under normal distribution assumption, the VaR value is improper compared with the actual losses. The paper discuss three methods. Historical Simulated method - Variance-Covariance method and Mixture Normal .simulating those asset, return and VaR by given proper confidence level. About the Mixture Normal Distribution, we use both EM algorithm and Quasi-Bayesian MLE calculating its parameters. Finally, we use tree VaR testing methods, Back test、Forward tes and Binomial test -----comparing its VaR loss probability We find the following results: 1.Under 1% left-tail critical probability, asset return distribution has significant Fat-tail character. 2.Using Mixture Normal distribution we can catch more Fat-tail character precisely than the other two methods. 3.The kurtosis of Mixture Normal is close to the actual kurtosis, this means that the Mixture Normal distribution can catch the Leptokurtosis phenomenon. Key words: Value at Risk、VaR、Fat tail、Historical simulation method、 Variance-Covariance method、Mixture Normal distribution、Quasi-Bayesian MLE、EM algorithm、Back test、 Forward test、 Leptokurtosis