Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications

Nelson Vadori and Anatoliy Swishchuk
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Nelson Vadori: Department Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
Anatoliy Swishchuk: Department Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada

Mathematics, 2019, vol. 7, issue 5, 1-62

Abstract: The paper is devoted to the inhomogeneous random evolutions (IHRE) and their applications in finance. We introduce and present some properties of IHRE. Then, we prove weak law of large numbers and central limit theorems for IHRE. Financial applications are given to illiquidity modeling using regime-switching time-inhomogeneous Levy price dynamics, to regime-switching Levy driven diffusion based price dynamics, and to a generalized version of the multi-asset model of price impact from distress selling, for which we retrieve and generalize their diffusion limit result for the price process.

Keywords: propagators; inhomogeneous random evolutions; inhomogeneous semi-Markov process; weak law of large numbers; central limit theorem; orthogonal martingale measure; regime-switching time-inhomogeneous Levy price dynamics; multi-asset model of price impact from distress selling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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