Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

The Laplace Transform

Diffusion processes and their sample paths

This work considers the problem of quickest detection with N distributed sensors that receive sequential observations either in discrete or in continuous time from the environment. These sensors employ cumulative sum (CUSUM) strategies and communicate to a central fusion center by one shot schemes. One shot schemes are schemes in which the sensors communicate with the fusion center only once, via which they signal a detection. The communication is clearly asynchronous and the case is considered in which the fusion center employs a minimal strategy, which means that it declares an alarm when the first communication takes place. It is assumed that the observations received at the sensors are independent and that the time points at which the appearance of a signal can take place are different. Both the cases of the same and different signal distributions across sensors are considered. It is shown that there is no loss of performance of one shot schemes as compared to the centralized case in an extended Lorden min-max sense, since the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound. In the case of different signal distributions the optimal threshold parameters are explicitly computed.

One Shot Schemes for Decentralized Quickest Change Detection

Using the large deviation principle (LDP) for a rescaled fractional Brownian motion $B^H_t$, where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional stochastic volatility model of the form $dS_t=S_t\sigma(Y_t) (\bar{\rho} dW_t +\rho dB_t), \,dY_t=dB^H_t$, where $\sigma$ is $\alpha$-Holder continuous for some $\alpha\in(0,1]$; in particular, we show that $t^{H-\frac{1}{2}} \log S_t $ satisfies the LDP as $t\to0$ and the model has a well-defined implied volatility smile as $t \to 0$, when the log-moneyness $k(t)=x t^{\frac{1}{2}-H}$ Thus the smile steepens to infinity or flattens to zero depending on whether $H\in(0,\frac{1}{2})$ or $H\in(\frac{1}{2},1)$ We also compute large-time asymptotics for a fractional local-stochastic volatility model of the form $dS_t= S_t^{\beta} |Y_t|^p dW_t,dY_t=dB^H_t$, and we generalize two identities in Matsumoto and Yor [Probab Surv, 2 (2005), pp 312--347] to show that $\frac{1}{t^{2H}}\l

Asymptotics for Rough Stochastic Volatility Models

The drawdown of an asset is a risk measure defined in terms of the running maximum of the asset's spot price over some period [0, T]. The asset price is said to have drawn down by at least $K over this period if there exists a time at which the underlying is at least $K below its maximum-to-date. We introduce insurance against a large realization of maximum drawdown and a novel way to hedge the liability incurred by underwriting this insurance. Our proposed insurance pays a fixed amount should the maximum drawdown exceed some fixed threshold over a specified period. The need for this drawdown insurance would diminish should markets rise before they fall. Consequently, we propose a second kind of cheaper maximum drawdown insurance that pays a fixed amount contingent on the drawdown preceding a drawup. We propose double barrier options as hedges for both kinds of insurance against large maximum drawdowns. In fact for the second kind of insurance we show that the hedge is model-free. Since double barrier opt...

/pdf/maximum-drawdown-insurance-1vsbgfh6ss.pdf

Maximum drawdown insurance

June 30, 2015AbstractThis paper considers magnitude, asymptotics and duration of drawdowns for some L´evyprocesses. First, we revisit some existing results on the magnitude of drawdowns for spec-trally negative L´evy processes using an approximation approach. For any spectrally negativeL´evy process whose scale functions are well-behaved at 0+, we then study the asymptotics ofdrawdown quantities when the threshold of drawdown magnitude approaches zero. We alsoshow that such asymptotics is robust to perturbations of additional positive compound Poissonjumps. Finally, thanks to the asymptotic results and some recent works on the running max-imum of L´evy processes, we derive the law of duration of drawdowns for a large class of L´evyprocesses (with a general spectrally negative part plus a positive compound Poisson structure).The duration of drawdowns is also known as the “Time to Recover” (TTR) the historical max-imum, which is a widely used performance measure in the fund management industry. We ﬁndthat the law of duration of drawdowns qualitatively depends on the path type of the spectrallynegative component of the underlying L´evy process.Keywords: Asymptotics; Drawdown; Duration; L´evy process; Magnitude; Parisian stoppingtimeMSC(2000): Primary 60G40; Secondary 60G51

/pdf/on-magnitude-asymptotics-and-duration-of-drawdowns-for-levy-4tnvcx5h62.pdf

On magnitude, asymptotics and duration of drawdowns for Lévy models

In this paper we examine the probabilistic behavior of two quantities closely related to market crashes. The first is the drawdown of an asset and the second is the duration of time between the last reset of the maximum before the drawdown and the time of the drawdown. The former is the first time the current drop of an investor’s wealth from its historical maximum reaches a pre-specified level and has been used extensively as a path-dependent measure of a market crash in the financial risk management literature. The latter is the speed at which the drawdown occurs and thus provides a measure of how fast a market crash takes place. We call this the speed of market crash. In this work we derive the joint Laplace transform of the last visit time of the maximum of a process preceding the drawdown, the speed of market crash, and the maximum of the process under general diffusion dynamics. We discuss applications of these results in the pricing of insurance claims related to the drawdown and its speed. Our applications are developed under the drifted Brownian motion model and the constant elasticity of variance (CEV) model.

Hongzhong Zhang

Papers

One Shot Schemes for Decentralized Quickest Change Detection

Asymptotics for Rough Stochastic Volatility Models

Maximum drawdown insurance

On magnitude, asymptotics and duration of drawdowns for Lévy models

Drawdowns and the Speed of Market Crash