Self-similar models in risk theory
AbstractThis Ph.D. thesis is concerned with self-similar processes. In Chapter 2 we describe the classes of transformations leading from self-similar to stationary processes, and conversely. The relationship is used in Chapter 3 to characterize stable symmetric self-similar processes via their minimal integral representation. This leads to a unique decomposition of a symmetric stable self-similar process into three independent parts. The class of such processes appears to be quite broad and can stand as a basis of different risk models. In Chapter 4 we give examples of applications of self-similar processes in insurance risk modelling. In Chapter 5 we illustrate a test of self-similarity (namely variance-time plots) on DJIA index data in order to justify the use of self-similar processes in financial modelling. Last but not least we propose an alternative model for stock price movements incorporating a martingale which generates the same filtration as fractional Brownian motion.
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Bibliographic InfoPaper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/98/03.
Length: 52 pages
Date of creation: 1998
Date of revision:
Self-similar process; Risk theory; Lamperti transformation; Insurance; Option pricing;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
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- Weron, Aleksander & Mercik, Szymon & Weron, Rafal, 1999.
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Physica A: Statistical Mechanics and its Applications,
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- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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