Mathematical Modelling and Algorithms in Finance

Topics in Mathematical Finance Topics in Mathematical Finance

A Dissertation submitted for the Degree of Doctor of Philosophy To the memory of my mother Contents Preface iii 1 Introduction 1 1.1 Option pricing in discrete time 1 1.2 Option pricing in continuous time 4 1.3 The Black-Scholes model 8 1.4 Interest-rate models 9

Large deviations in mathematical finance ∗

The area of large deviations is a set of asymptotic results on rare events probabilities and a set of methods to derive such results. Large deviations theory is a very active field in applied probability, and finds important applications in finance, where questions related to extremal events play an increasingly major role. Financial applications are various, and range from Monte-Carlo methods ...

New Trends in Mathematical Finance

Applications to Mathematical Finance

We give an introduction to the theory of Mathematical Finance with special emphasis on the applications of Banach space theory. The introductary section presents on an informal and intuitive level some of the basic ideas of Mathematical Finance, in particular the notions of “No Arbitrage” and “equivalent martingale measures”. In section two we formalize these ideas in a mathematically rigorous ...

Mathematical tools for finance

This note deals with the basic mathematical tools commonly used in finance. Stochastic calculus and its applications will be presented. The best will be done to present both the PDE and the probabilistic approaches to finance. However, the focus will be mostly on (vanilla) option pricing and fixed income techniques won’t really be presented. For additional information such as Girsanov’s Theorem...