The Fundamental Theorem of Asset Pricing states-roughly speaking-that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingale measure for S. It turns out that it is quite hard to give precise and sharp versions of this theorem in proper generality, if one insists on modifying the concept of \no arbitrage" as little as possible...

The fact that the solution of a martingale problem for a diffusion process gives a weak solution of the corresponding Itô equation is well-known since the original work of Stroock and Varadhan. The result is typically proved by constructing the driving Brownian motion from the solution of the martingale problem and perhaps an auxiliary Brownian motion. This constructive approach is much more ch...

The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation. This phenomenon is most completely understood when the arguments are mutually independent random variables, and there exist several powerful complementary me...

We generalize the concept of the Wehrl entropy of quantum states which gives a basis–independent measure of their localization in phase space. We discuss the minimal values and the typical values of these Rényi–Wehrl entropies for pure states for spin systems. According to Lieb’s conjecture the minimal values are provided by the spin coherent states. Though Lieb’s conjecture remains unproven, w...

We derive a general formula for the futures price process without the restriction that the assets used in the future margin account are continuous and of finite variation. To do so, we model tradeable securities with dividends which are not necessarily cash dividends at fixed times or continuously paid dividends. A future contract can then be modelled as an asset which pays dividends but has ze...

Abstract. It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale problem is well-posed in the class of solutions which are continuous in probability. This extension is used to improve on a criterion for a probabi...

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Environmental changes and human activity threaten the fauna of many geographical areas. We exploit the entropy definition from thermodynamics to assess ecosystem stability. In particular, we study a minimal ecosystem on a lattice in which two species struggle for sur...

Clustering on categorical data streams is a relatively new field that has not received as much attention as static data and numerical data streams. One of the main difficulties in categorical data analysis is lacking in an appropriate way to define the similarity or dissimilarity measure on data. In this paper, we propose three dissimilarity measures: a point-cluster dissimilarity measure (base...

We propose a general equilibrium model for asset pricing that incorporates asymmetric information as the key element determining security prices. In our setting, the concepts of completeness, arbitrage, state price and equivalent martingale measure are extended to the case of asymmetric information. Our model shows that in a so-called quasi-complete market, agents with differential information ...