Advanced Mathematical Methods for Finance

by Julia Di Nunno (Editor), Bernt Øksendal (Editor)

Overview

This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, shastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Product Details

ISBN-13:	9783642184116
Publisher:	Springer Berlin Heidelberg
Publication date:	04/12/2011
Edition description:	2011
Pages:	536
Product dimensions:	6.30(w) x 9.20(h) x 1.40(d)

About the Author

Giulia Di Nunno and Bernt Øksendal are professors at the University of Oslo. Their work in shastic analysis, control, and mathematical finance is internationally highly appreciated. They have been chairing the leadership of the large European ESF funded networking program AMaMeF in financial mathematics.

Table of Contents

Dynamic risk measures.- Ambit processes and shastic partial differential equations.- Fractional processes as models in shastic finance.- Credit contagion in a long range dependent macroeconomic factor model.- Modeling information flows in financial markets.- An overview of comonotonicity and its applications in finance and insurance.- A general maximum principle for anticipative shastic control and applications to insider trading.- Analyticity of the Wiener-Hopf factors and valuation of exotic options in Levy models.- Optimal liquidation of a pairs trade.- A PDE-based approach or pricing mortgage-backed securities.- Nonparametric methods for volatility density estimation.- Fractional smoothness and applications in finance.- Liquidity models in continuous and discrete times.- Some new BSDE results for an infinite-horizon shastic control problem.- Functionals associated with gradient shastic flows and nonlinear SPDEs.- Fractional smoothness and applications in Finance modeled by F-doubly shastic Markov chains.- Exotic derivatives under shastic volatility models with jumps.- Asymptotics of HARA utility from terminal wealth under proportional transaction costs with decision lag or execution delay and obligatory diversification.