Advanced Mathematical Methods for Finance

1. Front Matter

   Pages I-VIII

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2. Dynamic Risk Measures

   • Beatrice Acciaio, Irina Penner

   Pages 1-34

3. Ambit Processes and Stochastic Partial Differential Equations

   • Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart

   Pages 35-74

4. Fractional Processes as Models in Stochastic Finance

   • Christian Bender, Tommi Sottinen, Esko Valkeila

   Pages 75-103

5. Credit Contagion in a Long Range Dependent Macroeconomic Factor Model

   • Francesca Biagini, Serena Fuschini, Claudia Klüppelberg

   Pages 105-132

6. Modelling Information Flows in Financial Markets

   • Dorje C. Brody, Lane P. Hughston, Andrea Macrina

   Pages 133-153

7. An Overview of Comonotonicity and Its Applications in Finance and Insurance

   • Griselda Deelstra, Jan Dhaene, Michèle Vanmaele

   Pages 155-179

8. A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading

   • Giulia Di Nunno, Olivier Menoukeu Pamen, Bernt Øksendal, Frank Proske

   Pages 181-221

9. Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models

   • Ernst Eberlein, Kathrin Glau, Antonis Papapantoleon

   Pages 223-245

10. Optimal Liquidation of a Pairs Trade

    • Erik Ekström, Carl Lindberg, Johan Tysk

    Pages 247-255

11. A PDE-Based Approach for Pricing Mortgage-Backed Securities

    • Marco Papi, Maya Briani

    Pages 257-291

12. Nonparametric Methods for Volatility Density Estimation

    • Bert van Es, Peter Spreij, Harry van Zanten

    Pages 293-312

13. Fractional Smoothness and Applications in Finance

    • Stefan Geiss, Emmanuel Gobet

    Pages 313-331

14. Liquidity Models in Continuous and Discrete Time

    • Selim Gökay, Alexandre F. Roch, H. Mete Soner

    Pages 333-365

15. Some New BSDE Results for an Infinite-Horizon Stochastic Control Problem

    • Ying Hu, Martin Schweizer

    Pages 367-395

16. Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEs

    • B. Iftimie, M. Marinescu, C. Vârsan

    Pages 397-415

17. Pricing and Hedging of Rating-Sensitive Claims Modeled by $\mathbb{F}$ -doubly Stochastic Markov Chains

    • Jacek Jakubowski, Mariusz Niewęgłowski

    Pages 417-453

18. Exotic Derivatives under Stochastic Volatility Models with Jumps

    • Aleksandar Mijatović, Martijn Pistorius

    Pages 455-508

19. Asymptotics of HARA Utility from Terminal Wealth under Proportional Transaction Costs with Decision Lag or Execution Delay and Obligatory Diversification

    • Lukasz Stettner

    Pages 509-536

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, 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.

• Calculus of variations
• Comonotonicity applied in finance
• Fractional processes in finance
• Mathematical finance reviewed
• Modeling of long and short range dependence
• Pricing and hedging
• Quantitative finance
• Stochastic control with finite and infinite horizon
• Stochastic finance
• Stochastic modeling in finance
• Stochastic partial differential equations
• data-driven science, modeling and theory building

• CMA, Department of Mathematics, University of Oslo, Oslo, Norway

  Giulia Di Nunno, Bernt Øksendal

Giulia Di Nunno and Bernt Øksendal are professors at the University of Oslo. Their work in stochastic 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.