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Pension models
Kalaš, Martin
The thesis is concerned with the problem of sustainable spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. We gradually build a model, which coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. Within the framework of our intuitive model, we apply the method of moment matching to derive an approximation for the probability of individual's retirement ruin. The accuracy of presented approximation is analyzed via extensive Monte Carlo simulations. A numerical case study using Czech data is provided, including calculated values for the probability of ruin and maximal sustainable spending rate under various combinations of wealth-to-spending ratios and investment portfolio characteristics.
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Pension models
Kalaš, Martin
The thesis is concerned with the problem of sustainable spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. We gradually build a model, which coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. Within the framework of our intuitive model, we apply the method of moment matching to derive an approximation for the probability of individual's retirement ruin. The accuracy of presented approximation is analyzed via extensive Monte Carlo simulations. A numerical case study using Czech data is provided, including calculated values for the probability of ruin and maximal sustainable spending rate under various combinations of wealth-to-spending ratios and investment portfolio characteristics.
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Some quantitative aspects of life annuities
Šťástka, Petr ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee)
The aim of this diploma thesis is describe the most common methods of financing pension plans, focusing on some of the methods of fund financing pension plans. To describe the individual methods, their numerical illustration and allow comparison, it is necessary to dispose of necessary instruments. Therefore in the thesis there are constructed the cohort life tables for the Czech Republic. The thesis also deals with the modelling life annuities in continuous time, in particular, with the shape of im- mediate pension anuity factor for Gompertz law of mortality. Namely, this factor is one of the parameters entering the calculation of the individual methods of fund fi- nancing for pension plans.
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Penzijní modely
Kalaš, Martin ; Cipra, Tomáš (advisor) ; Branda, Martin (referee)
The thesis is concerned with the problem of sustainable spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. We gradually build a model, which coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. Within the framework of our intuitive model, we apply the method of moment matching to derive an approximation for the probability of individual's retirement ruin. The accuracy of presented approximation is analyzed via extensive Monte Carlo simulations. A numerical case study using Czech data is provided, including calculated values for the probability of ruin and maximal sustainable spending rate under various combinations of wealth-to-spending ratios and investment portfolio characteristics.
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