Bounded short-rate models with Ehrenfest and Jacobi processes [Elektronische Ressource] / vorgelegt von Alexander Kaplun

Bounded short-rate modelswith Ehrenfest and JacobiprocessesDISSERTATIONzur Erlangung des Gradeseines Doktors der Naturwissenschaftender Fakult at fur Mathematikder Technischen Universit at Dortmundvorgelegt vonDipl.-Math. Alexander KaplunDortmund, Juli 2010Betreuer: Prof. Dr. M. VoitTo my parentsNatalia and Iakovpoblagovasdcaaserivsegovaxeotzdarditeli,terpenieoRdderku.AcknowledgmentsFirst, I would like to thank my thesis adviser Prof. Dr. Michael Voit for hisinvaluable support and for suggesting this interesting topic to me. He gaveme guidance throughout the development of this thesis, as well as during mygraduate and undergraduate studies, starting with the very rst course incalculus.I am very thankful to Prof. Dr. Jeanette Woerner for the advice that shegave to me, both of a mathematical and of a professional nature.I wholeheartedly thank Silvetta for her love and inspiration. I am deeplyindebted and grateful to my parents Natalia and Iakov for giving me un-conditional support throughout my life and encouragement to pursue mygoals.ContentsIntroduction 11 Special functions and orthogonal polynomials 41.1 Hypergeometric functions of a matrix argument . . . . . . . . 41.2 Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . 61.3 Jacobi polynomials . . . . . . . . . . . . . . . . . . . . . . . . 72 Introduction to interest rate modelling 112.1 Basics of nancial modelling . . . . . . . . . . . . . . . . . . .