Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains.
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Part I: Mathematical Models 1. On Model Risk 2. Robust Optimization Problems in Finance 3. A Survey of Stochastic Portfolio Theory 4. Stochastic Volatility Modeling and Use of Perturbation Methods 5. Downside and Drawdown Risk Characteristics of Optimal Continuous Time 6. Portfolio of Choice and Valuation in Incomplete Markets 7. Integration by Parts Formulas for Levy Processes Application in Finance
Part II: Computational Methods 8. On the Discrete Time Capital Asset Pricing Model 9. Quantization Methods and Applications to Numerical Problems in Finance 10. Recombining Binomial Tree Approximations for Diffusions 11. Computational Methods for Calibration 12. Numerical Methods in Finance: Monte Carlo Methods
Part III: Applications 13. Real Options 14. Anticipative Stochastic Control for Levy Processes with Application to Insider Trading 15. Functional Quantization and Applications to the Pricing of Path-Dependent Derivatives. 16. Stochastic Clock in Financial Markets 17. Exotic Options 18. Filtering a Regime Switching VG Price Process