Prof. Dr. Anatoliy Swishchuk
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
'%3e%3cpath%20d='M22.1642%2019.0924C21.7317%2018.068%2021.1041%2017.1375%2020.3163%2016.3527C19.5309%2015.5656%2018.6006%2014.9381%2017.5766%2014.5048C17.5674%2014.5002%2017.5582%2014.4979%2017.5491%2014.4933C18.9774%2013.4616%2019.9059%2011.7811%2019.9059%209.88504C19.9059%206.74408%2017.3611%204.19922%2014.2201%204.19922C11.0792%204.19922%208.53429%206.74408%208.53429%209.88504C8.53429%2011.7811%209.46282%2013.4616%2010.8912%2014.4956C10.882%2014.5002%2010.8728%2014.5025%2010.8636%2014.5071C9.83652%2014.9404%208.91487%2015.5617%208.1239%2016.355C7.33685%2017.1404%206.70933%2018.0707%206.276%2019.0947C5.85031%2020.0972%205.62072%2021.172%205.59967%2022.2609C5.59905%2022.2853%205.60335%2022.3097%205.61229%2022.3325C5.62123%2022.3553%205.63465%2022.376%205.65174%2022.3935C5.66883%2022.4111%205.68926%2022.425%205.71182%2022.4345C5.73437%2022.444%205.7586%2022.4489%205.78308%2022.4489H7.15868C7.25956%2022.4489%207.3398%2022.3686%207.3421%2022.2701C7.38795%2020.5001%208.09868%2018.8425%209.35506%2017.5861C10.655%2016.2862%2012.3814%2015.5709%2014.2201%2015.5709C16.0588%2015.5709%2017.7852%2016.2862%2019.0852%2017.5861C20.3415%2018.8425%2021.0523%2020.5001%2021.0981%2022.2701C21.1004%2022.3709%2021.1807%2022.4489%2021.2815%2022.4489H22.6571C22.6816%2022.4489%2022.7058%2022.444%2022.7284%2022.4345C22.751%2022.425%2022.7714%2022.4111%2022.7885%2022.3935C22.8056%2022.376%2022.819%2022.3553%2022.8279%2022.3325C22.8369%2022.3097%2022.8412%2022.2853%2022.8406%2022.2609C22.8176%2021.165%2022.5907%2020.0989%2022.1642%2019.0924ZM14.2201%2013.8284C13.1678%2013.8284%2012.1773%2013.418%2011.4322%2012.6729C10.6871%2011.9278%2010.2767%2010.9374%2010.2767%209.88504C10.2767%208.83271%2010.6871%207.84227%2011.4322%207.09715C12.1773%206.35204%2013.1678%205.94165%2014.2201%205.94165C15.2724%205.94165%2016.2629%206.35204%2017.008%207.09715C17.7531%207.84227%2018.1635%208.83271%2018.1635%209.88504C18.1635%2010.9374%2017.7531%2011.9278%2017.008%2012.6729C16.2629%2013.418%2015.2724%2013.8284%2014.2201%2013.8284Z'%20fill='%238590A2'/%3e%3c/g%3e%3c/svg%3e)
Co-authors
Following
Followers
Research Focus & Metrics
Explore full metrics on Scilit
Academic Career Length
19Years (2008-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications
Journal Article
Anatoliy SwishchukAHAiden Huffman
Aiden HuffmanIn this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regard to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.
2 February 2015 in Stochastic Analysis and Applications
Journal Article
NVN. Vadori
N. VadoriAnatoliy SwishchukLimit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of Pyke Schaufele (Limit theorems for Markov renewal processes, Ann. Math. Statist., 35(4):1746–1764, 1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example, in finance and insurance. Unfortunately, no limit theorems have been obtained for functionals of inhomogeneous Markov renewal and semi-Markov processes as of today, to the best of the authors’ knowledge. In this article, we provide strong law of large numbers and central limit theorem results for such processes. In particular, we make an important connection of our results with the theory of ergodicity of inhomogeneous Markov chains. Finally, we provide an application to risk processes used in insurance by considering a inhomogeneous semi-Markov version of the well-known continuous-time Markov chain model, widely used in the literature.
Journal Article
Anatoliy SwishchukWe show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital (risk process) of an insurance company with the amount of claims described by the risk model based on GCHP. The main approach in both cases is to use functional central limit theorem for the GCHP to approximate it with a diffusion process. Then we construct and solve Hamilton–Jacobi–Bellman (HJB) equation for the expected utility function. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.
1 June 2019 in Methodology and Computing in Applied Probability
Journal Article
JCJonathan A. Chávez-Casillas
Jonathan A. Chávez-CasillasRERobert J. Elliott
Robert J. ElliottBRBruno Remillard
Bruno RemillardAnatoliy SwishchukJournal Article
ACAna Roldan Contreras
Ana Roldan ContrerasAnatoliy SwishchukThe present paper is focused on the solution of optimal control problems such as optimal acquisition, optimal liquidation, and market making in relation to the high-frequency trading market. We have modeled optimal control problems with the price approximated by the diffusion process for the general compound Hawkes process (GCHP), using results from the work of Swishchuk and Huffman. These problems have been solvedusing a price process incorporating the unique characteristics of the GCHP. The GCHP was designed to reflect important characteristics of the behaviour of real-world price processes such as the dependence on the previous process and jumping features. In these models, the agent maximizes their own utility or value function by solving the Hamilton–Jacobi–Bellman (HJB) equation and designing a strategy for asset trading. The optimal solutions are expressed in terms of parameters describing the arrival rates and the midprice process from the price process, modeled as a GCHP, allowing such characteristics to influence the optimization process, aiming towards the attainment of a more general solution. Implementations of the obtained results were carried out using real LOBster data.
26 June 2017 in SSRN Electronic Journal
Preprint
Anatoliy SwishchukIn this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN) and the Functional Central Limit Theorem (FCLT) are proved. We also study the main properties of this new risk model, net profit condition, premium principle and ruin time (including ultimate ruin time) applying the LLN and FCLT for the RMGCHP. We show similar results for risk model based on compound Hawkes process (RMCHP) and apply them to the classical risk model based on compound Poisson process (RMCPP).
About Me
Dr. Anatoliy Swishchuk is a professor in mathematical finance at the Department of Mathematics and Statistics, University of Calgary, Calgary, Canada. He received his B.Sc. and M.Sc. degrees from Kyiv State University, Kyiv, Ukraine. He is a holder of two doctorate degrees in Mathematics and Physics (Ph. D. and D. Sc.) from the prestigious National Academy of Sciences of Ukraine (NASU), Kiev, Ukraine, and is a recipient of the NASU award for young scientists, with a gold medal for series of research publications in random evolutions and their applications. Dr. Swishchuk is a chair and organizer of finance and energy finance seminar ’Lunch at the Lab’ at the Department of Mathematics and Statistics. Dr. Swishchuk is a Director of Mathematical and Computational Finance Laboratory at the University of Calgary. Dr. Swishchuk is a creator of the mathematical finance program at the Department of Mathematics & Statistics. He is also a proponent and creator of a new specialization, “Financial and Energy Markets Data Modelling”, in the Data Science and Analytics program. His research areas include financial mathematics, random evolutions and their applications, biomathematics, stochastic calculus, and he serves on editorial boards for several research journals. He is the author of more than 200 publications, including 17 books and more than 150 articles in peer-reviewed journals. In 2018, he received a Peak Scholar award.