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Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications

Department Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
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Mathematics 2019, 7(5), 447; https://doi.org/10.3390/math7050447
Received: 20 February 2019 / Revised: 19 April 2019 / Accepted: 5 May 2019 / Published: 19 May 2019
(This article belongs to the Special Issue New Trends in Random Evolutions and their Applications)
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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. View Full-Text
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 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Vadori, N.; Swishchuk, A. Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications. Mathematics 2019, 7, 447.

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