We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with...

We consider models for stock prices which relates to random pro cesses with independent homogeneous increments Levy processes These models are arbitrage free but correspond to the incomplete nancial market There are many di erent approaches for pricing of nancial derivatives We consider here mainly the approach which is based on minimal relative entropy This method is related to an utility func...

We establish many-server heavy-traffic limits for G/M/n + M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue-length process where the limit is an ordinary differential equation in a two-state random environment. With asymptotically negligible service interru...

We study a Monte Carlo algorithm for simulation of probability distributions based on stochastic step functions, and compare to the traditional Metropolis/Hastings method. Unlike the latter, the step function algorithm can produce an uncorrelated Markov chain. We apply this method to the simulation of Levy processes, for which simulation of uncorrelated jumps are essential. We perform numerical...

Title of dissertation: DEPENDENCE STRUCTURE IN LEVY PROCESSES AND ITS APPLICATION IN FINANCE Qiwen Chen, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dilip B. Madan Department of Finance In this paper, we introduce DSPMD, discretely sampled process with prespecified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified mar...

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at longer timescales. In this paper I further test the truncated Levy paradigm u...