Stochastic methods in finance: lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2004
|
| Schriftenreihe: | Lecture notes in mathematics
1856 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 306 S. 235 mm x 155 mm |
| ISBN: | 3540229531 |
Internformat
MARC
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| 245 | 1 | 0 | |a Stochastic methods in finance |b lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 |c K. Back ... Ed.: M. Frittelli ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XIII, 306 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1856 | |
| 650 | 4 | |a Finanzmathematik - Stochastisches Modell - Kongress - Brixen <2003> | |
| 650 | 4 | |a Finanzmathematik / Stochastischer Prozess / Theorie | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Stochastic analysis | |
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| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Back, Kerry E. |e Sonstige |0 (DE-588)129613835 |4 oth | |
| 700 | 1 | |a Frittelli, Marco |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| adam_text | Contents
Incomplete and Asymmetric Information in Asset Pricing
Theory
Kerry Back 1
1 Filtering Theory 1
1.1 Kalman Bucy Filter 3
1.2 Two State Markov Chain 4
2 Incomplete Information 5
2.1 Seminal Work 5
2.2 Markov Chain Models of Production Economies 6
2.3 Markov Chain Models of Pure Exchange Economies 7
2.4 Heterogeneous Beliefs 11
3 Asymmetric Information 12
3.1 Anticipative Information 12
3.2 Rational Expectations Models 13
3.3 Kyle Model 16
3.4 Continuous Time Kyle Model 18
3.5 Multiple Informed Traders in the Kyle Model 20
References 23
Modeling and Valuation of Credit Risk
Tomasz R. Bielecki, Monique Jeanblanc, Marek Rutkowski 27
1 Introduction 27
2 Structural Approach 29
2.1 Basic Assumptions 29
Defaultable Claims 29
Risk Neutral Valuation Formula 31
Defaultable Zero Coupon Bond 32
2.2 Classic Structural Models 34
Merton s Model 34
Black and Cox Model 37
2.3 Stochastic Interest Rates 43
X Contents
2.4 Credit Spreads: A Case Study 45
2.5 Comments on Structural Models 46
3 Intensity Based Approach 47
3.1 Hazard Function 47
Hazard Function of a Random Time 48
Associated Martingales 49
Change of a Probability Measure 50
Martingale Hazard Function 53
Defaultable Bonds: Deterministic Intensity 53
3.2 Hazard Processes 55
Hazard Process of a Random Time 56
Valuation of Defaultable Claims 57
Alternative Recovery Rules 59
Defaultable Bonds: Stochastic Intensity 63
Martingale Hazard Process 64
Martingale Hypothesis 65
Canonical Construction 67
Kusuoka s Counter Example 69
Change of a Probability 70
Statistical Probability 72
Change of a Numeraire 74
Preprice of a Defaultable Claim 77
Credit Default Swaption 79
A Practical Example 82
3.3 Martingale Approach 84
Standing Assumptions 85
Valuation of Defaultable Claims 85
Martingale Approach under (H.I) 87
3.4 Further Developments 88
Default Adjusted Martingale Measure 88
Hybrid Models 89
Unified Approach 90
3.5 Comments on Intensity Based Models 90
4 Dependent Defaults and Credit Migrations 91
4.1 Basket Credit Derivatives 92
The ?;th t.o Default Contingent Claims 92
Case of Two Entities 93
4.2 Conditionally Independent Defaults 94
Canonical Construction 94
Independent Default Times 95
Signed Intensities 96
Valuation of FDC and LDC 96
General Valuation Formula 97
Default Swap of Basket Type 98
Contents XI
4.3 Copula Based Approaches 99
Direct Application 100
Indirect Application 100
Simplified Version 102
4.4 Jarrow and Yu Model 103
Construction and Properties of the Model 103
Bond Valuation 105
4.5 Extension of the Jarrow and Yu Model 106
Kusuoka s Construction 107
Interpretation of Intensities 108
Bond Valuation 108
4.6 Dependent Intensities of Credit Migrations 109
Extension of Kusuoka s Construction 109
4.7 Dynamics of Dependent Credit Ratings 112
4.8 Defaultable Term Structure 113
Standing Assumptions 113
Credit Migration Process 116
Defaultable Term Structure 117
Premia for Interest Rate and Credit Event Risks 119
Defaultable Coupon Bond 120
Examples of Credit Derivatives 121
4.9 Concluding Remarks 122
References 123
Stochastic Control with Application in Insurance
Christian Hipp 127
1 Preface 127
2 Introduction Into Insurance Risk 128
2.1 The Lundberg Risk Model 128
2.2 Alternatives 129
2.3 Ruin Probability 129
2.4 Asymptotic Behavior For Ruin Probabilities 131
3 Possible Control Variables and Stochastic Control 132
3.1 Possible Control Variables 132
Investment, One Risky Asset 132
Investment, Two or More Risky Assets 133
Proportional Reinsurance 134
Unlimited XL Reinsurance 134
XL Reinsurance 135
Premium Control 135
Control of New Business 135
3.2 Stochastic Control 136
Objective Functions 136
Infinitesimal Generators 137
Hamilton Jacobi Bellman Equations 139
XII Contents
Verification Argument 141
Steps for Solution 143
4 Optimal Investment for Insurers 143
4.1 HJB and its Handy Form 143
4.2 Existence of a Solution 145
4.3 Exponential Claim Sizes 145
4.4 Two or More Risky Assets 147
5 Optimal Reinsurance and Optimal New Business 148
5.1 Optimal Proportional Reinsurance 150
5.2 Optimal Unlimited XL Reinsurance 151
5.3 Optimal XL Reinsurance 152
5.4 Optimal New Business 153
6 Asymptotic Behavior for Value Function and Strategies 154
6.1 Optimal Investment: Exponential Claims 154
6.2 Optimal Investment: Small Claims 154
6.3 Optimal Investment: Large Claims 155
6.4 Optimal Reinsurance 156
7 A Control Problem with Constraint: Dividends and Ruin 157
7.1 A Simple Insurance Model with Dividend Payments 157
7.2 Modified HJB Equation 158
7.3 Numerical Example and Conjectures 159
7.4 Earlier and Further Work 161
8 Conclusions 162
References 163
Nonlinear Expectations, Nonlinear Evaluations and Risk
Measures
Shige Peng 165
1 Introduction 165
1.1 Searching the Mechanism of Evaluations of Risky Assets 165
1.2 Axiomatic Assumptions for Evaluations of Derivatives 166
General Situations: ^ Consistent Nonlinear Evaluations 166
•F/^ Consistent Nonlinear Expectations 167
1.3 Organization of the Lecture 168
2 Brownian Filtration Consistent Evaluations and Expectations 169
2.1 Main Notations and Definitions 169
2.2 ^ Consistent Nonlinear Expectations 171
2.3 ^ Consistent Nonlinear Evaluations 173
3 Backward Stochastic Differential Equations: (^ Evaluations and
g Expectations 176
3.1 BSDE: Existence, Uniqueness and Basic Estimates 176
3.2 1 Dimensional BSDE 182
Comparison Theorem 183
Backward Stochastic Monotone Semigroups and ^ Evaluations . 186
Example: Black Scholes Evaluations 188
Contents XIII
^ Expectations 189
Upcrossing Inequality of £S Supermartingales and Optional
Sampling Inequality 193
3.3 A Monotonic Limit Theorem of BSDE 199
3.4 ^ Martingales and (Nonlinear) g Supermartingale
Decomposition Theorem 201
4 Finding the Mechanism: Is an ^ Expectation a ^ Expectation? 204
4.1 £M Dominated ^ Expectations 204
4.2 .^ Consistent Martingales 207
4.3 BSDE under ^ Consistent Nonlinear Expectations 210
4.4 Decomposition Theorem for £ Supermartingales 213
4.5 Representation Theorem
of an ^ Expectation by a ^ Expectation 216
4.6 How to Test and Find g? 219
4.7 A General Situation: ^ Evaluation Representation Theorem ... 220
5 Dynamic Risk Measures 221
6 Numerical Solution of BSDEs: Euler s Approximation 222
7 Appendix 224
7.1 Martingale Representation Theorem 224
7.2 A Monotonic Limit Theorem of Ito s Processes 226
7.3 Optional Stopping Theorem for £S Supermartingale 232
References 238
References on BSDE and Nonlinear Expectations 240
Utility Maximisation in Incomplete Markets
Walter Schachermayer 255
1 Problem Setting 255
2 Models on Finite Probability Spaces 259
2.1 Utility Maximization 266
The complete Case (Arrow) 266
The Incomplete Case 272
3 The General Case 277
3.1 The Reasonable Asymptotic Elasticity Condition 277
3.2 Existence Theorems 281
References 289
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| spelling | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 K. Back ... Ed.: M. Frittelli ... Berlin [u.a.] Springer 2004 XIII, 306 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1856 Finanzmathematik - Stochastisches Modell - Kongress - Brixen <2003> Finanzmathematik / Stochastischer Prozess / Theorie Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2003 Brixen gnd-content Finanzmathematik (DE-588)4017195-4 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Back, Kerry E. Sonstige (DE-588)129613835 oth Frittelli, Marco Sonstige oth Lecture notes in mathematics 1856 (DE-604)BV000676446 1856 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012955115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 Lecture notes in mathematics Finanzmathematik - Stochastisches Modell - Kongress - Brixen <2003> Finanzmathematik / Stochastischer Prozess / Theorie Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4017195-4 (DE-588)1071861417 |
| title | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 |
| title_auth | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 |
| title_exact_search | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 |
| title_full | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 K. Back ... Ed.: M. Frittelli ... |
| title_fullStr | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 K. Back ... Ed.: M. Frittelli ... |
| title_full_unstemmed | Stochastic methods in finance lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 K. Back ... Ed.: M. Frittelli ... |
| title_short | Stochastic methods in finance |
| title_sort | stochastic methods in finance lectures given at the c i m e e m s summer school held in bressanone brixen italy july 6 12 2003 |
| title_sub | lectures given at the C.I.M.E.-E.M.S. Summer School held in Bressanone/Brixen, Italy, July 6 - 12, 2003 |
| topic | Finanzmathematik - Stochastisches Modell - Kongress - Brixen <2003> Finanzmathematik / Stochastischer Prozess / Theorie Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik - Stochastisches Modell - Kongress - Brixen <2003> Finanzmathematik / Stochastischer Prozess / Theorie Mathematisches Modell Finance Mathematical models Stochastic analysis Stochastisches Modell Finanzmathematik Konferenzschrift 2003 Brixen |
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