发帖
雷达卡
Stochastic Differential Games - Theory and Applications.rar
(3.38 MB, 需要: 5 个论坛币)
本附件包括：- Stochastic Differential Games - Theory and Applications.pdf
Stochastic Differential Games. Theory and ApplicationsSeries: Atlantis Studies in Probability and Statistics, Vol. 2
Ramachandran, Kandethody M., Tsokos, Chris P.
2012, 2012, X, 248 p. 3 illus., 1 in color.
The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
Content Level » Graduate
Keywords » Competive advertising - Equity investment - Finance models - Game theory - Investor speculation
Related subjects » Applications - Game Theory / Mathematical Methods - Mathematics - Operations Research & Decision Theory - Probability Theory and Stochastic Processes
Contents
Preface vii
1. Introduction, Survey and Background Material 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 DeterministicDifferentialGames: ABriefSurvey . . . . . . . . . . . . . 5
1.3 Stochastic Differential Games: Definition and Brief Discussion . . . . . . 14
1.4 Formulation of theProblem. . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5 BasicDefinitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2. Stochastic Linear Pursuit-Evasion Game 25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Preliminaries and an Existence Theorem . . . . . . . . . . . . . . . . . . 26
2.3 Existence of a Solution for a Stochastic Linear Pursuit-Evasion Game . . 30
2.4 The Solution of a Stochastic Linear Pursuit-Evasion Game With
Nonrandom Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3. Two Person Zero-Sum Differential Games-General Case 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Two Person Zero-sum Games: Martingale methods . . . . . . . . . . . . 47
3.3 TwoPersonZero-sumGames andViscositySolutions . . . . . . . . . . . 58
3.4 Stochastic differential games with multiple modes . . . . . . . . . . . . . 61
4. Formal Solutions for Some Classes of Stochastic Linear Pursuit-
Evasion Games 65
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Formal solution for a Stochastic Linear Pursuit-Evasion game with
perfect information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
ix
x Stochastic Differential Games
4.4 On Stochastic Pursuit-Evasion games with imperfect information . . . . . 69
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5. N-Person Noncooperative Differential Games 73
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 A stochastic Pursuit-Evasion Game . . . . . . . . . . . . . . . . . . . . 73
5.3 General solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6. Weak Convergence in Two Player Stochastic Differential Games 95
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2 Weak Convergence Preliminaries . . . . . . . . . . . . . . . . . . . . . . 96
6.3 Some Popular Payoff Structures . . . . . . . . . . . . . . . . . . . . . . 98
6.4 Two Person Zero-sum Stochastic Differential Game with Multiple
Modes, Weak Convergence . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.5 Partially Observed Stochastic Differential Games . . . . . . . . . . . . . 125
6.6 Deterministic Approximations in Two-Person Differential Games . . . . 135
7. Weak Convergence in Many Player Games 147
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2 Some Popular Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.3 Deterministic Approximations in
N-Person Differential Games . . . . . . 1578. Some Numerical Methods 165
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.2 Discounted Payoff Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.3 Ergodic Payoff case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.4 Non-zeroSumCase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9. Applications to Finance 215
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
9.2 Stochastic Equity Investment Model with Institutional Investror
Speculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
9.3 Competitive Advertising under Uncertainty . . . . . . . . . . . . . . . . 221
References 233
京公网安备 11010802022788号
