A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

A comment on the Nash program and the theory of implementation

The mechanisms in the Nash program for cooperative games are madecompatible with the framework of the theory of implementation. This is donethrough a reinterpretation of the characteristic function that avoids feasibilityproblems, thereby allowing an analysis that focuses exclusively on the payoff space. In this framework, we show that the core is the only majorcooperative solution that is Maskin monotonic. Thus, implementation of mostcooperative solutions must rely on refinements of the Nash equilibrium concept(like most papers in the Nash program do). Finally, the mechanisms in theNash program are adapted into the model.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Intensity correlation function of dye lasers: Short-time behavior

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.

The use of tricyclic antidepressants in the treatment of temporomandibular joint disorders: systematic review of the literature of the last 20 years

Many therapies have been proposed for the management of temporomandibular disorders, including the use of different drugs. However, lack of knowledge about the mechanisms behind the pain associated with this pathology, and the fact that the studies carried out so far use highly disparate patient selection criteria, mean that results on the effectiveness of the different medications are inconclusive. This study makes a systematic review of the literature published on the use of tricyclic antidepressants for the treatment of temporomandibular disorders, using the SORT criteria (Strength of recommendation taxonomy) to consider the level of scientific evidence of the different studies. Following analysis of the articles, and in function of their scientific quality, a type B recommendation is given in favor of the use of tricyclic antidepressants for the treatment of temporomandibular disorders.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Embedding theorems of function classes, IV

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Embedding theorems of function classes, II

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The period function of the generalized Lotka-Volterra centers

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Embedding theorems of function classes, I

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The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Inequality and a repeated joint project

Agents voluntarily contribute to an infinitely repeated joint project. We investigate the conditions for cooperation to be a renegotiation-proof and coalition-proof equilibrium before examining the influence of output share inequality on the sustainability of cooperation. When shares are not equally distributed, cooperation requires agents to be more patient than under perfect equality. Beyond a certain degree of share inequality, full efficiency cannot be reached without redistribution. This model also explains the coexistence of one cooperating and one free-riding coalition. In this case, increasing inequality can have a positive or negative impact on the aggregate level of effort.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.