This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very highest quality papers in the field of financial mathematics.
Author(s): Jiro Akahori, Shigeyoshi Ogawa, Shinzo Watanabe
Edition: illustrated edition
Publisher: World Scientific Pub Co (
Year: 2002
Language: English
Pages: 309
CONTENTS......Page 12
Preface......Page 6
Program......Page 7
1. Introduction......Page 14
2. Additional Logarithmic Utility and Information Drift......Page 16
3. The Information Drift and the Law of Additional Information......Page 19
4. Additional Utility and Entropy of Filtrations......Page 29
References......Page 32
1. Introduction......Page 36
2. Comparison Results......Page 41
3. Uniform H¨older Continuities of Viscosity Solutions......Page 44
4. Other H¨older Continuities of Viscosity Solutions......Page 53
5. Strong Maximum Principle......Page 57
6. Ergodic Problem for Integro-di.erential Equations......Page 58
References......Page 64
1.1 Model-based vs model-free arbitrage......Page 66
2. Definitions and Notations......Page 70
3. Pricing Rules as Conditional Expectation Operators......Page 72
4.1 Implications for the specification of derivative pricing models......Page 75
4.3 Introduction of a set of benchmark assets......Page 76
References......Page 78
1. Introduction......Page 80
2.1 Notations and definitions......Page 82
2.2 Super-replication Theorem......Page 84
3. The Main Results......Page 85
4.1 Specification of the models......Page 89
4.2.1 Vanilla Options.......Page 90
4.2.3 Extension.......Page 91
5. Conclusion......Page 93
Appendix: Proof of Theorem 2.2......Page 94
References......Page 96
1. Introduction......Page 98
2.1 Mixed Brownian-Poisson process diffusion......Page 100
2.2 Optimal stopping problem......Page 101
2.3 Function φ......Page 102
3. Reflective diffusion......Page 104
References......Page 107
1. Introduction......Page 110
2. The Model and Some Basic Examples......Page 111
2.1 The affine case......Page 112
2.2 Examples......Page 113
2.2.2 Example 2. Recovery payment......Page 114
3. Incomplete Information (The Filtering Problem)......Page 115
3.2.1 Filter between defaults......Page 116
4. Filtering in Affine Models......Page 118
4.1 Filter between defaults......Page 119
4.2 Filter at a default time......Page 121
4.3 Filter algorithm......Page 122
5. Finite Dimensional Computation of the Filter......Page 123
References......Page 126
1. Introduction......Page 128
2. Definitions......Page 129
3. Main Results......Page 130
4. Applications......Page 135
5.1 When is the rough path property preserved?......Page 136
5.3 probabilistic versions of the First Theorem......Page 137
References......Page 138
1. Introduction......Page 140
2.1 Production in a network industry under imperfect competition......Page 142
2.2 A two-firm case......Page 143
3.1 Simultaneous investment......Page 144
3.2 Bypass equilibrium......Page 145
3.3 Access equilibrium......Page 147
4.1 Possible equilibria under open access policy......Page 148
4.2 A follower’s choice of strategy......Page 149
4.4 The equilibrium......Page 151
5.2 The e.ect on a follower’s entry timing......Page 153
5.3 The e.ect on a leader’s entry timing......Page 154
6. Uncertainty’s e.ect on the choice of competition regimes......Page 155
Appendix The derivation of a single firm’s value function in the case of simultaneous investment......Page 156
References......Page 162
1. Introduction......Page 164
2.1 A Basic Mode......Page 168
2.2 Derivation of the Project Values......Page 172
3.1 Selection of parameters......Page 175
3.2 Project values under the condition of FMA......Page 177
3.4 Discontinuity between FMA and SMA......Page 180
4. Concluding Remarks......Page 183
References......Page 184
1. Introduction......Page 186
2. Average Strike Put Options......Page 188
3. American Average Strike Put Options......Page 190
4. Average Strike Put Options of the Game Type......Page 194
5. Early Exercise Premium and Early Cancellation Fee......Page 198
6. Appendix: A Generalized Ito's Formula and Local Time of a One Dimensional Stochastic Flow......Page 200
References......Page 204
1. Problems and Results......Page 206
References......Page 209
1. Introduction......Page 210
2. Higher order methods for weak approximations of SDEs......Page 211
3. High order recombination for evolving stochastic systems......Page 214
4. A measure support reduction algorithm......Page 215
5. A second algorithm......Page 218
6. Some results from cubature onWiener space......Page 221
7. Cubature with recombination......Page 224
8. Application of the recombination methods to the stochastic filtering problem......Page 227
References......Page 230
1. Introduction......Page 232
2. A Verification Theorem......Page 238
References......Page 244
1. Introduction and Prelimilaries......Page 246
2. The Cartersian Product of Kingman Convolution Algebras......Page 248
3. Multivariate Symmetric RandomWalks......Page 252
References......Page 256
1. Introduction, Notation and Preliminaries......Page 258
2.3 The general case α > 0 :......Page 262
3. Mappings {U(α)
c } and Classes {Uα(X)}......Page 263
4. Stochastic Representation of MSDPM’s and s-MSDPM’s.......Page 264
5. An Application in Option Pricing......Page 268
References......Page 270
1. Introduction......Page 272
2. Verification of Solow model......Page 275
3. The stochastic Solow equation......Page 276
4. A quaere to Inada condition......Page 279
References......Page 287
1. Introduction......Page 288
2.2 Filter evolution......Page 291
3.1 Optimal stopping......Page 292
3.2 Control problems......Page 293
4. Short Background on Optimal Vector Quantization......Page 294
5. Quantization of the Filter Process......Page 296
6.1 Quantization of optimal stopping......Page 298
References......Page 309
