The validity of the classic Black-Scholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In ...

The concepts of semimartingales and their characteristic triples are introduced for stochastic processes taking their values in a locally compact second countable abelian group. It is proved that the third characteristic always exists and that the first two characteristics always exist when the group is compact. Any continuous additive Gaussian process in a locally compact second countable abel...

This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance. The ...

We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration generated by the process, in the framework of Vershik’s theory of filtrations. Non-standardness indicates the presence of long memory in a purely probabilistic sense. We aim to provide a short, n...

We construct a stochastic process whose drift is a function of the process’s local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in [7]. We construct and give asymptotic results for two different arrangements of inert particles and Brownian particles, and construct the analogous process in R.

We construct a continuous bounded stochastic process (St)t2[0;1] which admits an equivalent martingale measure but such that the minimal martingale measure in the sense of Follmer and Schweizer does not exist. This example also answers (negatively) a problem posed by I. Karatzas, J. P. Lehozcky and S. E. Shreve as well as a problem posed C. Stricker.

We compare two different definitions for the wavelet entropy associated to stochastic processes. In order to understand their advantages and disadvantages, exact results obtained for fractional Gaussian noise (−1 < α < 1) and the fractional Brownian motion (1 < α < 3) are assessed. We find out that NTWS family performs better as a characterization method for these stochastic processes.

Many seasonal macroeconomic time series are subject to changes in their means and variances over a long time horizon. In this paper we propose a general treatment for the modelling of time-varying features in economic time series. We show that time series models with mean and variance functions depending on dynamic stochastic processes can be sufficiently robust against changes in their dynamic...

We are dealing with regression models for point processes having a multiplicative intensity process of the form (t) b t. The deterministic function describes the long-term trend of the process. The stochastic process b accounts for the short-term random variations and depends on a nite-dimensional parameter. The semiparametric estimation procedure is based on one single observation over a long ...

This study investigates the extent of the contribution of the original GARCH model to our understanding of the stochastic process underlying exchange rate price changes, and examines if the movement of current research to GARCH type models exclusively is warranted. GARCH(1,1) parameters are calculated on a yearly basis and used to standardize the exchange rate price change data. Frequency distr...