We investigate quantitatively the so-called leverage effect, which corresponds to a negative correlation between past returns and future volatility. For individual stocks, this correlation is moderate and decays exponentially over 50 days, while for stock indices, it is much stronger but decays faster. For individual stocks, the magnitude of this correlation has a universal value that can be ra...

We review all recent contributions to the literature on stochastic processes. In particular, the Relativistic OrnsteinUhlenbeck Process is presented in detail, as is the intrinsic Brownian motion studied by Franchi and Le Jan. The Relativistic Brownian Motion of Dunkel and Hänggi is also reviewed, together with a model introduced by Oron and Horwitz. We finally suggest some possible future deve...

We present two new stochastic–volatility models in which option prices for European plain vanilla options have closed–form expressions. The models are motivated by the wellknown SABR model but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox– Ingersoll–Ross process and a geometric Brownian motio...

Series representations are obtained for the entire class of measurable, second order stochastic processes defined on any interval of the real line. They include as particular cases all earlier representations; they suggest a notion of "smoothness" that generalizes well known continuity notions; and they decompose the stochastic process into two orthogonal parts, the smooth part and a strongly d...

We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state dependence. The limit stochastic process is a continuous-path reflected process on the nonnegative orthant. We give an application to generalised Jackson networks with...

In this paper we introduce a concept of asymptotic log-likelihood ratio as a measure of deviation of the joint distribution from the product of their margins, we give the generalized strong law of large numbers (strong law expressed by inequalities, i.e. strong deviation theorems) for stochastic process indexed by a tree. As corollaries, we obtain some known results.

A necessary and suucient condition is given to reduce a non-stationary random process fZ(t) : t 2 T Rg to stationarity via a bijective diieren-tiable time deformation so that its correlation function r(t; t 0) depends only on the diierence (t 0)?(t) through a stationary correlation function R: r(t; t 0) = R(((t 0) ? (t)).

Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O’Connell [Math. Proc. Cambridge Philos. Soc. (...

In a recent paper the author used his work in measure and integration to obtain the projective limit theorem of Kolmogorov in a comprehensive version in terms of inner premeasures. In the present paper the issue is the influence of the new theorem on the notion of stochastic processes. It leads to essential improvements in the foundation of special processes, of the Wiener process in the previo...