arXiv subjects

Carsten Chong

Publications and source records attributed to Carsten Chong.

21 records · Page 2Linked to original sources

arXiv2015

Integrability conditions for space-time stochastic integrals: Theory and applications

We derive explicit integrability conditions for stochastic integrals taken over time and space driven by a random measure. Our main tool is a canonical decomposition of a random measure which extends the results from the purely temporal case. We show that the characteristics of this decomposition can be chosen as predictable strict random measures, and we compute the characteristics of the stochastic integral process. We apply our conditions to a variety of examples, in particular to ambit processes, which represent a rich model class.

math.PR↗

arXiv2015

Simulation of stochastic Volterra equations driven by space--time Lévy noise

In this paper we investigate two numerical schemes for the simulation of stochastic Volterra equations driven by space--time Lévy noise of pure-jump type. The first one is based on truncating the small jumps of the noise, while the second one relies on series representation techniques for infinitely divisible random variables. Under reasonable assumptions, we prove for both methods $L^p$- and almost sure convergence of the approximations to the true solution of the Volterra equation. We give explicit convergence rates in terms of the Volterra kernel and the characteristics of the noise. A simulation study visualizes the most important path properties of the investigated processes.

math.PR↗

arXiv2014

Superposition of COGARCH processes

We suggest three superpositions of COGARCH (supCOGARCH) volatility processes driven by Lévy processes or Lévy bases. We investigate second-order properties, jump behaviour, and prove that they exhibit Pareto-like tails. Corresponding price processes are defined and studied. We find that the supCOGARCH models allow for more flexible autocovariance structures than the COGARCH. Moreover, other than most financial volatility models, the supCOGARCH processes do not exhibit a deterministic relationship between price and volatility jumps. Furthermore, in one supCOGARCH model not all volatility jumps entail a price jump, while in another supCOGARCH model not all price jumps necessarily lead to volatility jumps.

math.PR↗