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Bibliographic Details
Main Author:	Kunz, Andreas 1974- (Author)
Format:	Book
Language:	English
Published:	2002
Subjects:	Extremwert Extremwertstatistik Diffusionsprozess Portfolio Selection Finanzmathematik Risikomanagement Asymptotik Spektralanalyse > Stochastik Hochschulschrift
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010119365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	München, Techn. Univ., Diss., 2002
Physical Description:	VIII, 159 S. graph. Darst.

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adam_text	CONTENTS ACKNOWLEDGEMENT I ABSTRACT VII 1 INTRODUCTION 1 1.1 CLASSICAL EXTREME VALUE THEORY AND BEYOND. 2 1.2 OBJECTIVE AND SETUP. 6 1.3 MAIN RESULTS AND OUTLINE OF THE THESIS. 10 2 LARGE FLUCTUATIONS 15 2.1 WEAK SOLUTIONS AND EMBEDDING IN L 2-SPACES. 16 2.2 EXPLOITING THE EIGENVALUE ASYMPTOTICS. 18 2.3 UNIFORMLY ELLIPTIC REVERSIBLE DIFFUSIONS. 23 3 PRELIMINARIES 25 3.1 WEAK SOLUTIONS AND EMBEDDING IN L 2-SPACES. 26 3.2 SOME TOPICS OF SPECTRAL ANALYSIS. 28 3.3 UNIFORMLY ELLIPTIC REVERSIBLE DIFFUSIONS. /.31 4 THE EUCLIDEAN CASE 35 4.1 MAIN RESULT AND PROOF. 36 4.2 EXAMPLES.41 4.2.1 THE ROTATIONALLY SYMMETRIC CASE .42 4.2.2 NON-SYMMETRIC PROCESSES.43 4.2.3 A DIFFUSION PROCESS WITH GAMMA DISTRIBUTION. 46 III BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/966050789 IV CONTENTS 4.2.4 THE ORNSTEIN-UHLENBECK PROCESS . 49 4.2.5 A COUNTEREXAMPLE. 53 5 THE LEVEL SET CASE 57 5.1 MAIN RESULT AND PROOF. 58 5.2 EXAMPLES. 63 5.2.1 THE ROTATIONALLY SYMMETRIC CASE. 64 5.2.2 NON-SYMMETRIC PROCESSES . 67 5.2.3 A POTENTIAL OF TETRAGONAL SHAPE. 71 6 SINGULAR PERTURBATIONS METHODS 75 6.1 RESCALING AND SINGULAR PERTURBATIONS. . 76 6.2 MAIN RESULT AND PROOF. 79 6.3 EXAMPLES. 84 6.3.1 THE ROTATIONALLY SYMMETRIC CASE. 84 6.3.2 NON-SYMMETRIC PROCESSES. 85 6.3.3 A DIFFUSION PROCESS WITH GAMMA DISTRIBUTION. 86 7 APPLICATIONS TO FINANCE 89 7.1 INTRODUCTION. 89 7.2 GRADIENT FIELD MODELS AND THEIR LARGE FLUCTUATIONS .91 7.3 MULTIVARIATE SHORT-RATE MODELS. 94 7.3.1 VASICEK MODEL. 94 7.3.2 EXPONENTIAL PROCESS . 96 7.3.3 GAMMA PROCESS. 97 7.4 PARAMETER ESTIMATION .100 7.4.1 ESTIMATION OF O .101 7.4.2 ESTIMATION OF $.102 7.5 THE GOODNESS-OF-FIT TESTS.104 7.6 APPLICATION TO SIMULATED AND FINANCIAL DATA.107 7.6.1 VASICEK MODEL.107 CONTENTS V 7.6.2 EXPONENTIAL PROCESS .ILL APPENDIX A CALCULATIONS FOR THE MAXIMUM ASYMPTOTICS 117 A.L EXPONENTIAL PROCESS .117 A.2 GAMMA PROCESS.119 B TABLES FOR ESTIMATION AND TEST RESULTS 125 BIBLIOGRAPHY 133 LIST OF FIGURES 141 LIST OF TABLES 144 LIST OF SYMBOLS 149 INDEX 153 CURRICULUM VITAE 155
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spellingShingle	Kunz, Andreas 1974- Extremes of multidimensional stationary diffusion processes and applications in finance Extremwert (DE-588)4137272-4 gnd Extremwertstatistik (DE-588)4153429-3 gnd Diffusionsprozess (DE-588)4274463-5 gnd Portfolio Selection (DE-588)4046834-3 gnd Finanzmathematik (DE-588)4017195-4 gnd Risikomanagement (DE-588)4121590-4 gnd Asymptotik (DE-588)4126634-1 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd
subject_GND	(DE-588)4137272-4 (DE-588)4153429-3 (DE-588)4274463-5 (DE-588)4046834-3 (DE-588)4017195-4 (DE-588)4121590-4 (DE-588)4126634-1 (DE-588)4056125-2 (DE-588)4113937-9
title	Extremes of multidimensional stationary diffusion processes and applications in finance
title_auth	Extremes of multidimensional stationary diffusion processes and applications in finance
title_exact_search	Extremes of multidimensional stationary diffusion processes and applications in finance
title_full	Extremes of multidimensional stationary diffusion processes and applications in finance Andreas Kunz
title_fullStr	Extremes of multidimensional stationary diffusion processes and applications in finance Andreas Kunz
title_full_unstemmed	Extremes of multidimensional stationary diffusion processes and applications in finance Andreas Kunz
title_short	Extremes of multidimensional stationary diffusion processes and applications in finance
title_sort	extremes of multidimensional stationary diffusion processes and applications in finance
topic	Extremwert (DE-588)4137272-4 gnd Extremwertstatistik (DE-588)4153429-3 gnd Diffusionsprozess (DE-588)4274463-5 gnd Portfolio Selection (DE-588)4046834-3 gnd Finanzmathematik (DE-588)4017195-4 gnd Risikomanagement (DE-588)4121590-4 gnd Asymptotik (DE-588)4126634-1 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd
topic_facet	Extremwert Extremwertstatistik Diffusionsprozess Portfolio Selection Finanzmathematik Risikomanagement Asymptotik Spektralanalyse Stochastik Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010119365&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT kunzandreas extremesofmultidimensionalstationarydiffusionprocessesandapplicationsinfinance

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