We consider the optimal mass transportation problem in R with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability result for this map, with respect to the space variable and to the parameter. The proof needs to establish the measurability of some set-valued mappings, related ...

In this paper we consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the recent literature, we provide necessary and sufficient conditions ...

Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow p(k) ∼ ck−α. We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network’s heterogeneity. Optimization of scale-free netw...

The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence of the positive invariant measure with density is established and a weak form of Foguel alternative proven. We show the equivalence among self-adjoint of the ...

We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than ε, converges as ε ↓ 0 in law to the regular μ-ary tree, where μ is the essential minimum of the offspring distribution. This gives an example of entropic repulsion where the limit has no entropy.

We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jum...

The paper presents a nancial market model that generates stochastic volatility using a minimal set of factors These factors formed by transformations of square root processes model the dynamics of di erent denominations of a benchmark portfolio Benchmarked prices are assumed to be local martin gales Numerical results for the pricing and hedging of basic derivatives on indices are described for ...

Using the idea of local entropy theory, we characterize sequence tuple via mean forms sensitive in both topological and measure-theoretical senses. For sense, show that for an ergodic measure-preserving system, $\mu$-sequence tuple, $\mu$-mean $\mu$-sensitive coincide, give example to ergodicity condition is necessary. a certain class minimal systems, tuple.

We introduce the partial martingale difference correlation, a scalar-valued measure of conditional mean dependence of Y given X, adjusting for the nonlinear dependence on Z, where X, Y and Z are random vectors of arbitrary dimensions. At the population level, partial martingale difference correlation is a natural extension of partial distance correlation developed recently by Székely and Rizzo ...

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 poss...