Theoretical and Practical Applications of Probability Excursions in Brownian Motion, Risk Capital Stress Testing, and Hedging of Power Derivatives

Sammanfattning: The thesis treats three different areas; (i) Ranked increments of stable processes and ranked excursions of Brownian motion, (ii) Sufficient capital levels for banks, and (iii) Trading strategies for reduction of the fluctuations of revenues for power plants.The first part is a theoretcial investigation involved with the calculation of distribution functions concerning special properties of stable processes. The second part is a description of a framework in which the sufficiency of capital levels for banks can be evaluated.The third part is a typical example of how financial mathematics can be used to derive practical methods applicable in risk management of energy derivatives and real options.Altogether, five papers are presented.