Editorial: Long-Memory Models in Mathematical Finance

Mathematical finance: basic models and unsolved problems

Mathematical finance is a relatively new mathematical field. It was in a phase of explosive growth last 10-15 years, and there is very indication it will continue growing for a while yet. The growth is due to a combination of demand from financial institutions and a breakthrough in the mathematical theory of option pricing. The talk will outline basic mathematical theorems and ideas used here, ...

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 ...