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Acceleration of calculations in life insurance
Kuzminskaya, Kseniya ; Janeček, Martin (advisor) ; Vitali, Sebastiano (referee)
One of the major issues in practical calculation in life insurance - typically value of liabilities, value of the company, pricing,... - is that the calculations run times are very long. This work should investigate possible approaches how to speed up the calculation (cluster analysis, flexing,...). If the results are positive, it can have crucial practical applications 1
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Risk and ratio measures in portfolio optimization
Zelman, Juraj ; Kopa, Miloš (advisor) ; Vitali, Sebastiano (referee)
This thesis is focused on distortion risk measures and distortion reward-risk ratios. Firstly, we summarize the properties of these measures related to coherency axioms and stochastic dominance. We present the proofs and explain the assumptions for consistency of distortion risk measures with stochastic dominance. Furthermore, their relation to risk measures Value- at-Risk and Expected Shortfall is explained, and numerous examples of these measures are presented. Then, the basics of the theory of distortion reward-risk ratios are provided. The main theoretical result of this thesis is the proposition of the distortion reward-risk optimization model. We propose this model with the assumption of a discrete loss random variable that has realizations with equal probabilities. Lastly, we analyze and discuss the results and limitations of our implementation in the specialized optimization software GAMS on real financial data. As it turns out, the class of distortion risk measures is prospective because it allows us to re- weight probabilities in the distribution and to model the risk-aversion preferences.
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Micro-level stochastic claims reserving
Rathouský, Marek ; Pešta, Michal (advisor) ; Vitali, Sebastiano (referee)
This thesis covers, in detail, theoretical background of micro-level stochastic model, which includes definition and properties of non-homogeneous Poisson process. This the- ory is then applied to real data generated by MTPL portfolio. Estimates of provisions under micro-level stochastic model are calculated using ordinary Monte Carlo simula- tion method. Results obtained from micro-level stochastic model are compared to Mack Chain-ladder estimates. 1
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The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
Vitali, Sebastiano ; Tichý, Tomáš ; Kopa, Miloš
Options are often priced by Black and Scholes model by using artificial (and unobserved) volatility implied by option market prices. Since many options do not have their traded counterparts with the same maturity and moneyness, it is often needed to interpolate the volatility values. The general procedure of implied volatility extraction from market prices and subsequent smoothing can, however, lead to inconsistent values or even arbitrage opportunities. In this paper, a potential arbitrage area is studied in connection with the calendar bandwidth construction.
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Acceleration of calculations in life insurance
Kuzminskaya, Kseniya ; Janeček, Martin (advisor) ; Vitali, Sebastiano (referee)
One of the major issue for life insurance companies is proper and consistent valuation of liabilities. This thesis introduces the standard estimation methods used in practice and discussed the alternative methods, which might help to speed up these calculations. It studies two possible methods of acceleration of calcu- lations in life insurance: analytic function and cluster analysis. The outcome of these work is comparison of discussed methods applied on generated life insur- ance portfolio. All methods were applied on two possible insurance products. Comparison of the results is based on the calculation precision and time needed to process the liabilities of the insurance company's portfolio. 1
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Acceleration of calculations in life insurance
Kuzminskaya, Kseniya ; Janeček, Martin (advisor) ; Vitali, Sebastiano (referee)
One of the major issues in practical calculation in life insurance - typically value of liabilities, value of the company, pricing,... - is that the calculations run times are very long. This work should investigate possible approaches how to speed up the calculation (cluster analysis, flexing,...). If the results are positive, it can have crucial practical applications 1
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Comparison of statistical methods for the scoring models development
Mrázková, Adéla ; Vitali, Sebastiano (advisor) ; Kopa, Miloš (referee)
The aim of this thesis is to introduce and summarize the process of scoring model development in general and then basic statistical approaches used to resolve this problem, which are in particular logistic regression, neural networks and decision trees (random forests). Application of described methods on a real dataset provided by PROFI CREDIT Czech, a.s. follows, including discussion of some implementation issues and their resolution. Obtained results are discussed and compared.
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Multistage nested distance in stochastic optimization
Horejšová, Markéta ; Vitali, Sebastiano (advisor) ; Lachout, Petr (referee)
Multistage stochastic optimization is used to solve many real-life problems where decisions are taken at multiple times, e.g., portfolio selection problems. Such problems need the definition of stochastic processes, which are usually approxim- ated by scenario trees. The choice of the size of the scenario trees is the result of a compromise between the best approximation and the possibilities of the com- puter technology. Therefore, once a master scenario tree has been generated, it can be needed to reduce its dimension in order to make the problem computation- ally tractable. In this thesis, we introduce several scenario reduction algorithms and we compare them numerically for different types of master trees. A simple portfolio selection problem is also solved within the study. The distance from the initial scenario tree, the computational time, and the distance between the optimal objective values and solutions are compared for all the scenario reduction algorithms. In particular, we adopt the nested distance to measure the distance between two scenario trees. 1
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Acceleration of calculations in life insurance
Kuzminskaya, Kseniya ; Janeček, Martin (advisor) ; Vitali, Sebastiano (referee)
One of the major issues in practical calculation in life insurance - typically value of liabilities, value of the company, pricing,... - is that the calculations run times are very long. This work should investigate possible approaches how to speed up the calculation (cluster analysis, flexing,...). If the results are positive, it can have crucial practical applications 1
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