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

• Pubblicazione: New York, : Nova Science Publishers, c2008
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (374 p.)
• Disciplina: 332.64/53
• Soggetto topico: Options (Finance) - Prices - Mathematical models; Investments - Mathematical models
• Altri autori: EhrhardtMatthias
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- 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 Conditions -- 6.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-up -- 3.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 MATHEMATICS -- Abstract -- 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 -- Conclusion -- Acknowledgements -- 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 -- 3.Global in Space Computation -- 4.Optimal Investment Problem -- Conclusion -- Acknowledgements -- References -- FIXED DOMAIN TRANSFORMATIONS AND SPLIT-STEP FINITE DIFFERENCE SCHEMES FOR NONLINEAR BLACK-SCHOLES EQUATIONS FOR AMERICAN OPTIONS -- Abstract -- 1.Introduction -- 2.Volatility Models -- 3.The Fixed Domain Transformation -- 4.Numerical Solution -- 5.Comparison Study -- Conclusion -- Acknowledgements -- Appendix -- References -- PRICING HYDROELECTRIC POWER PLANTS WITH/WITHOUT OPERATIONAL RESTRICTIONS: A STOCHASTIC CONTROL APPROACH -- Abstract -- 1.Introduction -- 2.Hydroelectric Power Plant Valuation Problem. ; 3.Numerical Algorithms -- 4.Properties of the Numerical Schemes -- 5.Numerical Results -- Conclusion -- Acknowledgements -- References -- NUMERICAL SOLUTIONS OF CERTAIN NONLINEAR MODELS IN EUROPEAN OPTIONS ON A DISTRIBUTED COMPUTING ENVIRONMENT -- Abstract -- 1.Introduction -- 2.The Black-Scholes Equation -- 3.Numerical Solutions of the Black-Scholes Equation with Lin-ear Volatility -- 4.Nonlinear Volatility -- 5.Numerical Solutions of the Black-Scholes Equation with Non-linear Volatility -- 6.The Two Level Time-Domain Algorithm -- 7.Conclusion -- References -- PART IV.PARAMETER IDENTIFICATION(INVERSE PROBLEMS) -- CALIBRATION PROBLEMS IN OPTION PRICING -- Abstract -- 1.Introduction -- 2.The Calibration Problem -- 3.Analysis of the Optimal Control Problem -- 4.A Sequential Quadratic Programming Algorithm -- 5.Numerical Experiments -- Conclusion -- Acknowledgements -- References -- INDEX.
• Titolo autorizzato: Nonlinear models in mathematical finance
• ISBN: 1-60876-421-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910824761403321
• Lo trovi qui: Univ. Federico II