Interaction of capital market participants is a complicated dynamic process. A stochastic model is proposed to describe the dynamics to predict short-term stock price behaviors. Independent compound Poisson processes are introduced to describe the occurrences of market orders, limit orders, and cancellations of limit orders, respectively. Based on high-frequency observations of the limit order ...

We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type π(dx) = e γx ν(e x − 1) dx, where ν is the density of the stable Lévy measure and γ is a positive parameter which depends on its characteristics. These processes were introduced in [10] as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processe...

For fixed $r\geq 3$ and $n$ divisible by $r$, let ${\mathcal H}={\mathcal H}^r_{n,M}$ be the random $M$-edge $r$-graph on $V=\{1,\ldots ,n\}$; that is, H}$ is chosen uniformly from $M$-subsets of K}:={V \choose r}$ ($:= \{\mbox{$r$-subsets $V$}\}$). Shamir's Problem (circa 1980) asks, roughly, for what $M=M(n)$ likely to contain a perfect matching (that $n/r$ disjoint $r$-sets)? In 2008 Johan...