Advanced Mathematical Methods for Finance

by Di Nunno, Giulia; Oksendal, Bernt

• ISBN13: 9783642184116
• ISBN10: 3642184111
• Format: Hardcover
• Copyright: 2011-04-12
• Publisher: Springer Nature

Summary

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, stochastic 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, L#xE9;vy 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.

Table of Contents

Dynamic Risk Measures	p. 1
Ambit Processes and Stochastic Partial Differential Equations	p. 35
Fractional Processes as Models in Stochastic Finance	p. 75
Credit Contagion in a Long Range Dependent Macroeconomic Factor Model	p. 105
Modelling Information Flows in Financial Markets	p. 133
An Overview of Comonotonicity and Its Applications in Finance and Insurance	p. 155
A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading	p. 181
Analyticity of the Wiener-Hopf Factors and Valuation of Exotic Options in Lévy Models	p. 223
Optimal Liquidation of a Pairs Trade	p. 247
A PDE-Based Approach for Pricing Mortgage-Backed Securities	p. 257
Nonparametric Methods for Volatility Density Estimation	p. 293
Fractional Smoothness and Applications in Finance	p. 313
Liquidity Models in Continuous and Discrete Time	p. 333
Some New BSDE Results for an Infinite-Horizon Stochastic Control Problem	p. 367
Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEs	p. 397
Pricing and Hedging of Rating-Sensitive Claims Modeled by F-doubly Stochastic Markov Chains	p. 417
Exotic Derivatives under Stochastic Volatility Models with Jumps	p. 455
Asymptotics of HARA Utility from Terminal Wealth under Proportional Transaction Costs with Decision Lag or Execution Delay and Obligatory Diversification	p. 509
Table of Contents provided by Ingram. All Rights Reserved.