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Rafał Łochowski, Ph.D., D.Sc. (dr hab.)

Associate Professor
Warsaw School of Economics
Institute of Mathematical Economics
ul. Madalinskiego 6/8
02-513 Warszawa (Warsaw)
Poland

Office hours (winter semester 2024/2025): Thursdays, 1.30 p.m. - 2.30 p.m., room 9 building S. Please send me an e-mail message at least 2 hours before the meeting.

Associate Researcher
African Institute for Mathematical Sciences
6 Melrose Road, Muizenberg
Cape Town 7945, South Africa

email: rlocho@sgh.waw.pl or rafal@aims.ac.za or (preferred) rlocho314@gmail.com


For students/Dla studentów


My Preprints

(2023) (with P. Das, T. Matsuda and N. Perkowski) Level crossings of fractional Brownian motion arXiv link
(2022) (with M. Barski) Classification and calibration of affine models driven by independent Lévy processes arXiv link
(2007) Stopping time for Ornstein-Uhlenbeck process vs. stopping time for discrete AR(1) process pdf file

Selected papers

(2024) (with W. Bednorz and P. Das) Local times of deterministic paths and self-similar processes with stationary increments as normalized numbers of interval crossings accepted for publication in Annales de l’Institut Henri Poincaré, arXiv link

(2023) BDG inequalities and their applications for model-free continuous price paths with instant enforcement Modern Stochastics: Theory and Applications 10(4), (open access)

(2023) (with W. Bednorz) Estimates of moments and right and left tails of hitting times of Bessel processes Bernoulli Journal 29(3), arXiv link

(2023) (with L. Ch. Galane and F. J. Mhlanga) On SDEs with Lipschitz coefficients, driven by continuous, model-free martingales Electronic Communications in Probability 28, (open access)

(2022) (with W. Bednorz and R. Martynek) On optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes ESAIM - Probability and Statistics 26, (open access)

(2022) (with N. Perkowski and D. Prömel) One-dimensional game-theoretic differential equations International Journal of Approximate Reasoning 141, arXiv link

(2021) (with J. Obłój, D. J. Prömel and P. Siorpaes) Local times and Tanaka--Meyer formulae for cadlag paths Electronic Journal of Probability 26, (open access)

(2021) (with W. Bednorz and R. Martynek) On tails of symmetric and totally asymmetric alpha-stable distributions Probability and Mathematical Statistics 41, (open access)

(2019) Quadratic variation of cadlag semimartingales as a.s. limit of the normalized truncated variations Stochastics 91, arXiv link

(2018) (with L. Ch. Galane and F. J. Mhlanga) On the quadratic variation of the model-free price paths with jumps Lithuanian Mathematical Journal 58, arXiv link

(2018) (with N. Perkowski and D. J. Prömel) A superhedging approach to stochastic integration Stochastic Processes and their Applications 128, arXiv link

(2018) A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces Journal of Inequalities and Applications 2018 (open access)

(2017) On a generalisation of the Banach indicatrix theorem Colloquium Mathematicum 148, old arXiv versions

(2016) On the double Laplace transform of the truncated variation of a Brownian motion with drift LMS (London Mathematical Society) Journal of Computation and Mathematics 19 (open access)

(2015) A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality Journal of Inequalities and Applications 2015 (open access)

(2015) (with W. Bednorz) Integrability and Concentration of Sample Paths' Truncated Variation of Fractional Brownian Motions, Diffusions and Lévy processes, Bernoulli 21, arXiv link

(2015) (with R. Ghomrasni) The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition, Mathematical Methods in the Applied Sciences 38, arXiv link

(2015) (with M. Jeanblanc and W. Schatzschneider) Full cooperation applied to environmental improvements, Banach Center Publications 104, pdf file

(2014) On Pathwise Stochastic Integration with respect to Semimartingales, Probability and Mathematical Statistics 34 (open access)

(2014) (with R. Ghomrasni) Integral and local limit theorems for numbers of level crossings for diffusions, Electronic Journal of Probability 19 (open access)

(2013) On a Generalisation of the Hahn-Jordan Decomposition for Real Cadlag Functions, Colloquium Mathematicum 132, arXiv link

(2013) (with P. Miłoś) On truncated variation, upward truncated variation and downward truncated variation for diffusions, Stochastic Processes and their Applications 123, arXiv link

(2011) Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift - their characteristics and applications, Stochastic Processes and their Applications 121, arXiv link

(2010) Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift - their mean value and their applications, Banach Center Publ. Vol. 90(open access)

(2008) Truncated variation of Brownian motion with drift, Bull. Pol. Acad. Sci. Math. Vol. 56 (open access)

(2006) Moment and tail estimates for multidimensional chaos generated by symmetric random variables with logarithmically concave tails, Banach Center Publ. Vol. 72 (open access)

(2003) (with R. Latała) Tail and moment estimates for multidimensional chaos generated by positive random variables with logarithmically concave tails, Progress in Probab. Vol. 56

Selected talks

(2021) Talk presented at the conference Modern Stochastics: Theory and Applications V, Kyiv, Ukraine pdf file
(2019) Talk presented at the Journal Club, AIMS South Africa, Muizenberg, South Africa pdf file
(2018) Talk presented at the University of Oxford Mathematical and Computational Finance Seminar, Oxford pdf file
(2017) Talk presented at the University of Cape Town, Cape Town, South Africa pdf file
(2017) Talk presented at the AIMS South Africa, Muizenberg, South Africa pdf file
(2016) Talk presented at the University of Limpopo, Polokwane, South Africa pdf file
(2016) Talk presented at the workshop Fractality and Fractionality, The Lorentz Center, Leiden, The Netherlands pdf file
(2015) Talk presented at the Wrocław University of Technology, Wrocław, Poland pdf file (in Polish)
(2015) Talk presented at the 6. Forum Matematyków Polskich, Warszawa, Poland pdf file (in Polish)
(2015) Talk presented at the Workshop on Mathematical Finance and Related Issues, Osaka University, Osaka, Japan (invited speaker) pdf file
(2013) Talk presented at the Advances in Mathematics of Finance - 6th AMaMeF and Banach Center Conference, Warsaw, Poland link
(2013) Talk presented at the German-Polish Joint Conference on Probability and Mathematical Statistics, Torun, Poland pdf file
(2013) Talk presented at the University of Western Cape, Cape Town, South Africa pdf file
(2012) Talk presented at the 55th Annual Congress of the South African Mathematical Society, Stellenbosch, South Africa pdf file
(2012) Talk presented at the Berliner Kolloquium Wahrscheinlichkeitstheorie pdf file
(2011) Talk presented at the 5th International Conference on Stochastic Analysis and its Applications, Bonn University link
(2011) Talk presented at the IV Congreso Universitario de Actuaria, Huixquilucan, Mexico pdf file
(2010) Talk presented at the 5th International Workshop on Applied Probability, Madrid pdf file
(2010) Talk presented at the 11th International Conference on Quantitative Methods in Economics, Warsaw (in Polish) pdf file
(2009) Talk presented at the Uludag University, Bursa, Turkey pdf file
(2009) Talk given at the 5th National Conference - Actuarial Problems - Theory and Practice, Warsaw School of Economics (in Polish) pdf file
(2008) Talk given at the 10th National Conference on Probability, Bedlewo, Poland (in Polish) pdf file
(2006) Talk given at the seminar on financial and actuarial mathematics, Vienna University of Technology pdf file
(2005) Talk summarizing results on chaos, obtained by Prof. Latała's group pdf file



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My email address: rlocho314@gmail.com