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    Stochastic Differential Games. Theory and Applications [推廣有獎]

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    Stochastic Differential Games. Theory and Applications
    Series: 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 &raquo; Graduate
    Keywords &raquo; Competive advertising - Equity investment - Finance models - Game theory - Investor speculation
    Related subjects &raquo; 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 . . . . . . 157

    8. 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



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