Stochastic control in insurance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
[2008]
|
| Schriftenreihe: | Probability and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 254 Seiten Diagramme |
| ISBN: | 9781848000025 |
Internformat
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Datensatz im Suchindex
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| adam_text | HANSPETER SCHMIDLI STOCHASTIC CONTROL IN INSURANCE SPRINGER CONTENTS
PREFACE VII 1 STOCHASTIC CONTROL IN DISCRETE TIME 1 1.1 DYNAMIC
PROGRAMMING 1 1.1.1 INTRODUCTION 1 1.1.2 DYNAMIC PROGRAMMING 2 1.1.3 THE
OPTIMAL STRATEGY 4 1.1.4 NUMERICAL SOLUTIONS FOR T = OO 6 1.2 OPTIMAL
DIVIDEND STRATEGIES IN RISK THEORY 9 1.2.1 THE MODEL 9 1.2.2 THE OPTIMAL
STRATEGY 12 1.2.3 PREMIA OF SIZE ONE 16 1.3 MINIMISING RUIN
PROBABILITIES 20 1.3.1 OPTIMAL REINSURANCE 20 1.3.2 OPTIMAL INVESTMENT
24 2 STOCHASTIC CONTROL IN CONTINUOUS TIME 27 2.1 THE
HAMILTON-JACOBI-BELLMAN APPROACH 28 2.2 MINIMISING RUIN PROBABILITIES
FOR A DIFFUSION APPROXIMATION. . 34 2.2.1 OPTIMAL REINSURANCE 34 2.2.2
OPTIMAL INVESTMENT 39 2.2.3 OPTIMAL INVESTMENT AND REINSURANCE 42 2.3
MINIMISING RUIN PROBABILITIES FOR A CLASSICAL RISK MODEL 43 2.3.1
OPTIMAL REINSURANCE 44 2.3.2 OPTIMAL INVESTMENT 54 2.3.3 OPTIMAL
REINSURANCE AND INVESTMENT 64 XIV CONTENTS 2.4 OPTIMAL DIVIDENDS IN THE
CLASSICAL RISK MODEL 69 2.4.1 RESTRICTED DIVIDEND PAYMENTS 70 2.4.2
UNRESTRICTED DIVIDEND PAYMENTS 79 2.5 OPTIMAL DIVIDENDS FOR A DIFFUSION
APPROXIMATION 97 2.5.1 RESTRICTED DIVIDEND PAYMENTS 97 2.5.2
UNRESTRICTED DIVIDEND PAYMENTS 102 2.5.3 A NOTE ON VISCOSITY SOLUTIONS
104 3 PROBLEMS IN LIFE INSURANCE 113 3.1 MERTON S PROBLEM FOR LIFE
INSURERS 114 3.1.1 THE CLASSICAL MERTON PROBLEM 114 3.1.2 SINGLE LIFE
INSURANCE CONTRACT 122 3.2 OPTIMAL DIVIDENDS AND BONUS PAYMENTS 127
3.2.1 UTILITY MAXIMISATION OF DIVIDENDS 127 3.2.2 UTILITY MAXIMISATION
OF BONUS 132 3.3 OPTIMAL CONTROL OF A PENSION FUND 135 3.3.1 NO
CONSTRAINTS 136 3.3.2 FIXED 6 141 3.3.3 FIXED C 142 3.3.4 POWER LOSS
FUNCTION AND CR-G = 0 143 4 ASYMPTOTICS OF CONTROLIED RISK PROCESSES 147
4.1 MAXIMISING THE ADJUSTMENT COEFRCIENT 147 4.1.1 OPTIMAL REINSURANCE
148 4.1.2 OPTIMAL INVESTMENT 152 4.1.3 OPTIMAL REINSURANCE AND
INVESTMENT 153 4.2 CRAMER-LUNDBERG APPROXIMATIONS FOR CONTROLIED
CLASSICAL RISK MODELS 154 4.2.1 OPTIMAL PROPORTIONAL REINSURANCE 154
4.2.2 OPTIMAL EXCESS OF LOSS REINSURANCE 163 4.2.3 OPTIMAL INVESTMENT
165 4.2.4 OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT .... 171 4.3
THE HEAVY-TAILED CASE 174 4.3.1 PROPORTIONAL REINSURANCE 174 4.3.2
EXCESS OF LOSS REINSURANCE 179 4.3.3 OPTIMAL INVESTMENT 181 4.3.4
OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT .... 194 CONTENTS XV A
STOCHASTIC PROCESSES AND MARTINGALES 201 A.L STOCHASTIC PROCESSES 201
A.2 FILTRATION AND STOPPING TIMES 201 A.3 MARTINGALES 202 A.4 POISSON
PROCESSES 203 A.5 BROWNIAN MOTION 205 A.6 STOCHASTIC INTEGRALS AND ITO S
FORMULA 206 A.7 SOME TAIL ASYMPTOTICS 209 B MARKOV PROCESSES AND
GENERATORS 211 B.L DEFINITION OF MARKOV PROCESSES 211 B.2 THE GENERATOR
211 C CHANGE OF MEASURE TECHNIQUES 215 C.L INTRODUCTION 215 C.2 THE
BROWNIAN MOTION 216 C.3 THE CLASSICAL RISK MODEL 217 D RISK THEORY 219
D.L THE CLASSICAL RISK MODEL 220 D.L.L INTRODUCTION 220 D.1.2 SMALL
CLAIMS 221 D.1.3 LARGE CLAIMS 223 D.2 PERTURBED RISK MODELS 225 D.3
DIFFUSION APPROXIMATIONS 226 D.4 PREMIUM CALCULATION PRINCIPLES 227 D.5
REINSURANCE 228 E THE BLACK-SCHOLES MODEL 231 F LIFE INSURANCE 235 F.L
CLASSICAL LIFE INSURANCE 235 F.2 BONUS SCHEMES 237 F.3 UNIT-LINKED
INSURANCE CONTRACTS 238 REFERENCES 241 LIST OF PRINCIPAL NOTATION 251
INDEX 253
|
| adam_txt |
HANSPETER SCHMIDLI STOCHASTIC CONTROL IN INSURANCE SPRINGER CONTENTS
PREFACE VII 1 STOCHASTIC CONTROL IN DISCRETE TIME 1 1.1 DYNAMIC
PROGRAMMING 1 1.1.1 INTRODUCTION 1 1.1.2 DYNAMIC PROGRAMMING 2 1.1.3 THE
OPTIMAL STRATEGY 4 1.1.4 NUMERICAL SOLUTIONS FOR T = OO 6 1.2 OPTIMAL
DIVIDEND STRATEGIES IN RISK THEORY 9 1.2.1 THE MODEL 9 1.2.2 THE OPTIMAL
STRATEGY 12 1.2.3 PREMIA OF SIZE ONE 16 1.3 MINIMISING RUIN
PROBABILITIES 20 1.3.1 OPTIMAL REINSURANCE 20 1.3.2 OPTIMAL INVESTMENT
24 2 STOCHASTIC CONTROL IN CONTINUOUS TIME 27 2.1 THE
HAMILTON-JACOBI-BELLMAN APPROACH 28 2.2 MINIMISING RUIN PROBABILITIES
FOR A DIFFUSION APPROXIMATION. . 34 2.2.1 OPTIMAL REINSURANCE 34 2.2.2
OPTIMAL INVESTMENT 39 2.2.3 OPTIMAL INVESTMENT AND REINSURANCE 42 2.3
MINIMISING RUIN PROBABILITIES FOR A CLASSICAL RISK MODEL 43 2.3.1
OPTIMAL REINSURANCE 44 2.3.2 OPTIMAL INVESTMENT 54 2.3.3 OPTIMAL
REINSURANCE AND INVESTMENT 64 XIV CONTENTS 2.4 OPTIMAL DIVIDENDS IN THE
CLASSICAL RISK MODEL 69 2.4.1 RESTRICTED DIVIDEND PAYMENTS 70 2.4.2
UNRESTRICTED DIVIDEND PAYMENTS 79 2.5 OPTIMAL DIVIDENDS FOR A DIFFUSION
APPROXIMATION 97 2.5.1 RESTRICTED DIVIDEND PAYMENTS 97 2.5.2
UNRESTRICTED DIVIDEND PAYMENTS 102 2.5.3 A NOTE ON VISCOSITY SOLUTIONS
104 3 PROBLEMS IN LIFE INSURANCE 113 3.1 MERTON'S PROBLEM FOR LIFE
INSURERS 114 3.1.1 THE CLASSICAL MERTON PROBLEM 114 3.1.2 SINGLE LIFE
INSURANCE CONTRACT 122 3.2 OPTIMAL DIVIDENDS AND BONUS PAYMENTS 127
3.2.1 UTILITY MAXIMISATION OF DIVIDENDS 127 3.2.2 UTILITY MAXIMISATION
OF BONUS 132 3.3 OPTIMAL CONTROL OF A PENSION FUND 135 3.3.1 NO
CONSTRAINTS 136 3.3.2 FIXED 6 141 3.3.3 FIXED C 142 3.3.4 POWER LOSS
FUNCTION AND CR-G = 0 143 4 ASYMPTOTICS OF CONTROLIED RISK PROCESSES 147
4.1 MAXIMISING THE ADJUSTMENT COEFRCIENT 147 4.1.1 OPTIMAL REINSURANCE
148 4.1.2 OPTIMAL INVESTMENT 152 4.1.3 OPTIMAL REINSURANCE AND
INVESTMENT 153 4.2 CRAMER-LUNDBERG APPROXIMATIONS FOR CONTROLIED
CLASSICAL RISK MODELS 154 4.2.1 OPTIMAL PROPORTIONAL REINSURANCE 154
4.2.2 OPTIMAL EXCESS OF LOSS REINSURANCE 163 4.2.3 OPTIMAL INVESTMENT
165 4.2.4 OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT . 171 4.3
THE HEAVY-TAILED CASE 174 4.3.1 PROPORTIONAL REINSURANCE 174 4.3.2
EXCESS OF LOSS REINSURANCE 179 4.3.3 OPTIMAL INVESTMENT 181 4.3.4
OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT . 194 CONTENTS XV A
STOCHASTIC PROCESSES AND MARTINGALES 201 A.L STOCHASTIC PROCESSES 201
A.2 FILTRATION AND STOPPING TIMES 201 A.3 MARTINGALES 202 A.4 POISSON
PROCESSES 203 A.5 BROWNIAN MOTION 205 A.6 STOCHASTIC INTEGRALS AND ITO'S
FORMULA 206 A.7 SOME TAIL ASYMPTOTICS 209 B MARKOV PROCESSES AND
GENERATORS 211 B.L DEFINITION OF MARKOV PROCESSES 211 B.2 THE GENERATOR
211 C CHANGE OF MEASURE TECHNIQUES 215 C.L INTRODUCTION 215 C.2 THE
BROWNIAN MOTION 216 C.3 THE CLASSICAL RISK MODEL 217 D RISK THEORY 219
D.L THE CLASSICAL RISK MODEL 220 D.L.L INTRODUCTION 220 D.1.2 SMALL
CLAIMS 221 D.1.3 LARGE CLAIMS 223 D.2 PERTURBED RISK MODELS 225 D.3
DIFFUSION APPROXIMATIONS 226 D.4 PREMIUM CALCULATION PRINCIPLES 227 D.5
REINSURANCE 228 E THE BLACK-SCHOLES MODEL 231 F LIFE INSURANCE 235 F.L
CLASSICAL LIFE INSURANCE 235 F.2 BONUS SCHEMES 237 F.3 UNIT-LINKED
INSURANCE CONTRACTS 238 REFERENCES 241 LIST OF PRINCIPAL NOTATION 251
INDEX 253 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:43:50Z |
| indexdate | 2024-07-09T21:10:58Z |
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| isbn | 9781848000025 |
| language | English |
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| spelling | Schmidli, Hanspeter 1963- Verfasser (DE-588)133812987 aut Stochastic control in insurance Hanspeter Schmidli London Springer [2008] © 2008 XV, 254 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Probability and its applications Bank Mathematik Banks and banking Distribution (Probability theory) Mathematical optimization Mathematics Structural control (Engineering) Versicherungsmathematik (DE-588)4063194-1 gnd rswk-swf Versicherung (DE-588)4063173-4 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 gnd rswk-swf Stochastische Kontrolltheorie (DE-588)4263657-7 s Versicherung (DE-588)4063173-4 s DE-604 Versicherungsmathematik (DE-588)4063194-1 s Erscheint auch als Online-Ausgabe 978-1-8480-0003-2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016301195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmidli, Hanspeter 1963- Stochastic control in insurance Bank Mathematik Banks and banking Distribution (Probability theory) Mathematical optimization Mathematics Structural control (Engineering) Versicherungsmathematik (DE-588)4063194-1 gnd Versicherung (DE-588)4063173-4 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| subject_GND | (DE-588)4063194-1 (DE-588)4063173-4 (DE-588)4263657-7 |
| title | Stochastic control in insurance |
| title_auth | Stochastic control in insurance |
| title_exact_search | Stochastic control in insurance |
| title_exact_search_txtP | Stochastic control in insurance |
| title_full | Stochastic control in insurance Hanspeter Schmidli |
| title_fullStr | Stochastic control in insurance Hanspeter Schmidli |
| title_full_unstemmed | Stochastic control in insurance Hanspeter Schmidli |
| title_short | Stochastic control in insurance |
| title_sort | stochastic control in insurance |
| topic | Bank Mathematik Banks and banking Distribution (Probability theory) Mathematical optimization Mathematics Structural control (Engineering) Versicherungsmathematik (DE-588)4063194-1 gnd Versicherung (DE-588)4063173-4 gnd Stochastische Kontrolltheorie (DE-588)4263657-7 gnd |
| topic_facet | Bank Mathematik Banks and banking Distribution (Probability theory) Mathematical optimization Mathematics Structural control (Engineering) Versicherungsmathematik Versicherung Stochastische Kontrolltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016301195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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