Nonlinear models in mathematical finance : new research trends in option pricing / Matthias Ehrhardt, editor.

Includes bibliographical references and index.

NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING; NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING; CONTENTS; PREFACE NONLINEAR MODELS IN OPTION PRICING; ABSTRACT; INTRODUCTION; PART I: NONLINEAR BLACK-SCHOLES MODELS; PART II: ANALYTIC SOLUTIONS; PART III: NUMERICAL TREATMENT OF NONLINEAR BLACK-SCHOLES EQUATIONS; PART IV: PARAMETER IDENTIFICATION (INVERSE PROBLEMS); NONLINEAR MODELS IN OPTION PRICING -- AN INTRODUCTION; Abstract; 1. Introduction; 2. Financial Derivatives; 3. Linear Black-Scholes Equations; 4. Nonlinear Black-Scholes Equations.

5. Terminal and Boundary Conditions6. Volatility Models; Conclusion; Acknowledgements; Appendix; A. Stochastics; B. Pricing Formulae; References; PART I. NONLINEAR BLACK-SCHOLES MODELS; OPTION PRICING AND HEDGING IN THE PRESENCE OF TRANSACTION COSTS AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; Abstract; 1. Introduction; 2. Modelling the Transaction Costs; 3. The Leland's Approach to Option Pricing and Hedging; 4. Utility-Based Option Pricing and Hedging; 5. Conclusion; Acknowledgements; References; UTILITY INDIFFERENCE PRICING WITH MARKET INCOMPLETENESS; Abstract; 1. Introduction.

2. Utility-Based Pricing and Hedging: The General Set-up3. Basis Risk Model; 4. Partial Information Basis Risk Model; Conclusion; Acknowledgements; References; PART II. ANALYTIC SOLUTIONS; PRICING OPTIONS IN ILLIQUID MARKETS: SYMMETRY REDUCTIONS AND EXACT SOLUTIONS; Abstract; 1. Introduction; 2. Illiquid Markets and Nonlinear Black-Scholes Equations; 3. Invariant Solutions for a Nonlinear Black-Scholes Equation; 4. Properties of Solutions and Parameter-Sensitivity; Conclusion; Acknowledgements; References.

DISTRIBUTIONAL SOLUTIONS TO AN INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM ARISING IN FINANCIAL MATHEMATICSAbstract; 1. Introduction; 2. Solutions for the Integro-Differential Problem (3); 3. Solutions for the Convolution Problem (8); Acknowledgements; References; PART III. NUMERICAL TREATMENT OF NONLINEARBLACK-SCHOLES EQUATIONS; A SEMIDISCRETIZATION METHOD FOR SOLVING NONLINEAR BLACK-SCHOLES EQUATIONS: NUMERICAL ANALYSIS AND COMPUTING; Abstract; 1. Introduction; 2. Numerical Schemes Construction; 3. Numerical Analysis about Local in Time Models; 4. Numerical Analysis about Global in Time Models.

ConclusionAcknowledgements; References; TRANSFORMATION METHODS FOR EVALUATING APPROXIMATIONS TO THE OPTIMAL EXERCISE BOUNDARY FOR LINEAR AND NONLINEAR BLACK-SCHOLES EQUATIONS; Abstract; 1. Introduction; 2. Risk Adjusted Methodology Model; 3. Transformation Method for a Linear Black-Scholes Equa-tion; 4. Transformation Method for a Nonlinear Black-Scholes Equation; 5. Transformation Methods for Asian Call Options; Conclusion; Acknowledgements; References; GLOBAL IN SPACE NUMERICAL COMPUTATION FOR THE NONLINEAR BLACK-SCHOLES EQUATION; Abstract; 1. Introduction; 2. Transaction Costs Model.

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