Non-Markov rate kernels: Application to batch auction

44 Pages Posted: 27 Oct 2021

See all articles by Martin Smid

Martin Smid

Institute of Information Theory and Automation, Prague

Aleš Kuběna

Institute of Information Theory and Automation of the CAS CZ

Date Written: October 25, 2021

Abstract

We introduce a theoretical tool for handling pure-jump processes taking values in complex spaces. We generalize the notion of rate kernels for the non-Markov case, being able to describe any pure-jump process in Borel space with absolutely continuous conditional distribution of jump times. We study the case of two simultaneously running processes where the evolution of the first is locally unaffected on the values of the second; we show that then the conditional distribution of the second can be evaluated as if the first were deterministic. Further we study pure-jump process of bounded atomic measures. We characterize rate kernels ruling processes of completely random atomic measures. Finally, we apply our theory to the model of call auction with the limit order process depending on a common driving factor called fair price; we give analytical formula for the conditional distribution of the order books given the trajectory of the fair price and semi-analytical formulas for both the conditional and unconditional distribution of the settlement price.

Keywords: pure-jump process, non-Markov rate kernels, atomic measures \sep completely random measures, batch auction

JEL Classification: C65,C57

Suggested Citation

Smid, Martin and Kuběna, Aleš, Non-Markov rate kernels: Application to batch auction (October 25, 2021). Available at SSRN: https://ssrn.com/abstract=3949374 or http://dx.doi.org/10.2139/ssrn.3949374

Martin Smid (Contact Author)

Institute of Information Theory and Automation, Prague ( email )

Pod vodarenskou vezi 4
Praha, CZ-18208
Czech Republic

HOME PAGE: http://www.klec.cz/martin

Aleš Kuběna

Institute of Information Theory and Automation of the CAS CZ ( email )

Pod vodarenskou vezi 4
Praha, CZ-18208
Czech Republic

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