Some Problems in Mathematical Finance

Abstract

This thesis discusses some problems in mathematical finance driven by Brownian motion, which is the basis for a large part of the modern probability theory that has been mentioned in the first chapter and which plays a crucial role in financial and statistical applications. The Brownian motion also became increasingly important in other mathematical aspects such as partial differential equations and differential geometry. Chapter two includes different constructions of Brownian motion and properties of Brownian paths. Chapters three and four include the results in mathematical finance and some applications, such as the discussion of the hedging strategies for contingent T-claims (e.g. European and Asian options) in Black and Scholes Market as well as some examples.