Research
Research
"Critical branching processes with immigration: scaling limits of local extinction sets" (A. Mijatović, B. Povar and G. Uribe Bravo) YouTube: Part 1: Results & Part 2: Proofs, arXiv:2503.20923
"Central limit theorem for superdiffusive reflected Brownian motion" (A. Mijatović, I. Sauzedde and A. Wade) Youtube, arXiv:2412.14267
"Limit Theorems for Stochastic Gradient Descent with Infinite Variance" (Jose Blanchet, A. Mijatović and Wenhao Yang) arXiv:2410.16340
"Superdiffusive limits for Bessel-driven stochastic kinetics" (M. Brešar, C. da Costa, A. Mijatović and A.R. Wade) YouTube, arXiv:2401.11863
"Modeling of Measurement Error in Financial Returns Data" (A. Jasra, A. Mijatović and M. Maama) arXiv:2408.07405
"Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat", to appear in Annals of Applied Probability (M. Brešar and A. Mijatović) YouTube: Part 1: tempared Langevin diffusions & Part 2: general results, arXiv:2408.13799
"Asymptotically optimal Wasserstein couplings for the small-time stable domain of attraction" (J. González Cázares, David Kramer-Bang and A. Mijatović), to appear in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques (2025), 39 pp., Youtube, arXiv:2411.03609
"Stationary entrance chains and applications to random walks" (A. Mijatović and V. Vysotskiy), to appear in Stochastic Processes and their Applications (2025), 36 pp., arXiv:2403.00619
"Fast exact simulation of the first-passage event of a subordinator" (J. González Cázares, F. Lin and A. Mijatović), to appear in Stochastic Processes and their Applications (2025), 25 pp., YouTube, arXiv:2306.06927, GitHub Python and Julia implementation
"Subexponential lower bounds for f-ergodic Markov processes" (M. Brešar and A. Mijatović), to appear in Probability Theory and Related Fields (2025), 58 pp., YouTube: Results & Proofs, arXiv:2403.14826
"Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function" (J. González Cázares, F. Lin and A. Mijatović) Stochastic Systems 15(1): 50-87 (2024) YouTube, arXiv:2303.11964 , GitHub with implementation in Python and Julia
"Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability" (M. Brešar, A. Mijatović and A.R. Wade) Annals of Probability 53(1): 175-222 (2025) YouTube, arXiv:2303.06916
"A weak MLMC scheme for Lévy-copula-driven SDEs with applications to the pricing of credit, equity and interest rate derivatives" (A. Mijatović and R. Palfray) Applied Mathematical Finance Vol. 31, No. 2, 57–107 (2024) arXiv:2211.02528
"When is the convex hull of a Lévy path smooth?" (D. Bang, J. I. Gonzáles Cázares and A. Mijatović) Annales de l’Institut Henri Poincaré - Probabilités et Statistiques Vol. 60, No 4, 2352–2381 (2024) YouTube, arXiv:2205.14416.
"Optimal Markovian coupling for finite activity Lévy processes" (W.S. Kendall, M. B. Majka and A. Mijatović), Bernoulli, 30(4): 2821-2845 (2024) arXiv:2210.11251
"How smooth can the convex hull of a Lévy path be?" (D. Bang, J. I. Gonzáles Cázares and A. Mijatović), Electronic Journal of Probability, 29: 1-36 (2024), YouTube, arXiv:2206.09928.
"Hölder continuity of the convex minorant of a Lévy process" (D. Bang, J. I. Gonzáles Cázares and A. Mijatović), Electronic Communications in Probability, 28: 1-12 (2023), YouTube, arXiv:2206.12433.
"Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity" (M. V. Menshikov, A. Mijatović and A. R. Wade), Annales de l’Institut Henri Poincaré - Probabilités et Statistiques Vol. 59, No. 4 (2023) 1813–1843 YouTube, arXiv:2203.00966.
"Joint density of a stable process and its supremum: regularity and upper bounds" (J. I. Gonzáles Cázares, A. Kohatsu Higa and A. Mijatović), Bernoulli 29(4), 3443-3469 (2023) YouTube, arXiv:2008.01894.
"Monte Carlo algorithm for the extrema of tempered stable processes" (J. I. Gonzáles Cázares and A. Mijatović), Advances in Applied Probability 55 (4) , 1362-1389 (2023) YouTube, arXiv:2103.15310.
"Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation" (J. I. Gonzáles Cázares and A. Mijatović), Finance & Stochastics, Vol. 26 (2022), 671–732 YouTube, arXiv:2011.06618.
"Asymptotic shape of the concave majorant of a Lévy process" (D. Bang, J. I. Gonzáles Cázares and A. Mijatović), Annales Henri Lebesgue, Vol. 5 (2022), 779-811 YouTube, arXiv:2106.09066.
"Limit theorems for local times and applications to SDEs with jumps" (A. Mijatović and G. Uribe Bravo), Stochastic Processes and their Applications, Vol. 153, 39-55 (2022), ResearchGate (results in this paper are mostly contained in the manuscript arXiv:1910.09501).
"Convex minorants and the fluctuation theory of Lévy processes" (J. I. Gonzáles Cázares and A. Mijatović), ALEA, Lat. Am. J. Probab. Math. Stat., 19, 983–999 (2022) YouTube, arXiv:2105.15060.
“Geometrically Convergent Simulation of the Extrema of Lévy Processes” (J. I. Gonzáles Cázares, A. Mijatović and G. Uribe Bravo), Mathematics of Operations Research 47(2):1141-1168, (2021) YouTube, arXiv:1810.11039.
"A Gaussian approximation theorem for Lévy processes" (D. Bang, J. I. Gonzáles Cázares and A. Mijatović), Statistics & Probability Letters, Vol. 178 (Nov 2021), arXiv:2104.13855.
"Monte Carlo estimation of the solution of fractional partial differential equations" (V. Kolokoltsov, F. Lin and A. Mijatović), Fractional Calculus and Applied Analysis, Vol. 24, no. 1, 278-306 (2021), arXiv:2012.13904.
"Lévy processes on smooth manifolds with a connection" (A. Mijatović and V. Mramor), Electronic Journal of Probability, 26: 1-39 (2021), YouTube, arXiv:2012.11633.
"An algorithm for simulating Brownian increments on a sphere" (A. Mijatović, V. Mramor and G. Uribe Bravo), Journal of Physics A: Mathematical and Theoretical Vol. 54, no. 11 (2021) arXiv:2012.12018.
“Stability of overshoots of zero mean random walks” (A. Mijatović and V. Vysotskiy), Electronic Journal of Probability, 25: 1-22 (2020), arXiv:1812.05909.
"ε -strong simulation of the convex minorants of stable processes and meanders" (J. I. Gonzáles Cázares, A. Mijatović and G. Uribe Bravo), Electronic Journal of Probability, 25: 1-33 (2020) arXiv:1910.13273.
“A note on the exact simulation of spherical Brownian motion” (A. Mijatović, V. Mramor and G. Uribe Bravo), Statistics & Probability Letters, Vol 165, (October 2020) arXiv:1811.12107.
“Non-asymptotic bounds for sampling algorithms without log-concavity” (M. Majka, A. Mijatović and L. Szpruch), Annals of Applied Probability, Vol. 30, no. 4, pp. 1534-1581 (2020), arXiv:1808.07105.
“Exact Simulation of the Extrema of Stable Processes” (J. I. Gonzáles Cázares, A. Mijatović and G. Uribe Bravo), Advances in Applied Probability, 51(4), 967-993 (2019) arXiv:1806.01870. GitHub with implementation in Python (by Vinayak Niraj) and Julia (by J. I. Gonzáles Cázares)
“Asymptotic variance for random walk Metropolis chains in high dimensions: logarithmic growth via the Poisson equation” (A. Mijatović and J. Vogrinc), Advances in Applied Probability, 51(4), 994-1026 (2019) arXiv:1707.08510.
“Invariance principle for non-homogeneous random walks” (N. Georgiou, A. Mijatović and A. Wade), Electronic Journal of Probability, 24:1-38 (2019) arxiv:1801.07882
“Projections of spherical Brownian motion” (A. Mijatović, V. Mramor and G. Uribe Bravo), Electronic Communications in Probability Vol. 23 (2018), 12 pp, arXiv:1806.00266.
“On the Poisson equation for Metropolis-Hastings chains” (A. Mijatović and J. Vogrinc), Bernoulli Vol. 24, no. 3 (2018), 2401–2428
“A radial invariance principle for non-homogeneous random walks” (N. Georgiou, A. Mijatović and A. Wade), Electronic Communications in Probability Vol. 23 (2018), 11 pp.
“Procuring load curtailment from local customers under uncertainty” (A. Mijatović, J. Moriarty and J. Vogrinc), Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (August 2017), doi: 10.1098/rsta.2016.0311
"Anomalous recurrence properties of many-dimensional zero-drift random walks" (N. Georgiou, M. Menshikov, A. Mijatović and A. Wade), Advances in Applied Probability Vol. 48, no. A (2016), 99--118
“Joint asymptotic distribution of certain path functionals of the reflected process” (A. Mijatović and M. Pistorius), Electronic Communications in Probability Vol. 21 (2016), 1–18
“Brownian manifolds, negative type and geo-temporal covariances” (N. H. Bingham, A. Mijatović and T. Symons), Communications on Stochastic Analysis Vol. 10, no. 4 (2016)
“A new look at short-term implied volatility in asset price models with jumps” (A. Mijatović and P. Tankov), Mathematical Finance Vol. 26, Issue 1 (January 2016), 149–183
“An integral equation for Root’s barrier and the generation of Brownian increments” (P. Gassiat, A. Mijatović and H. Oberhauser), Annals of Applied Probability Vol. 25, no. 4 (2015), 2039–2065
“Coupling and tracking of regime-switching martingales ” (S. D. Jacka and A. Mijatović), Electronic Journal of Probability Vol. 20 (2015), 39pp.
“Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications” (A. Mijatović, M. Pistorius and J. Stolte), Journal of Applied Probability Vol. 52, Issue 4 (December 2015), 1076–1096
“Markov chain approximations to scale functions of Lévy processes” (A. Mijatović, M. Vidmar and S. D. Jacka), Stochastic Processes and their Applications Vol. 125, Issue 10 (October 2015), 3932– 3957
“On the loss of the semimartingale property at the hitting time of a level” (A. Mijatović and M. Urusov), Journal of Theoretical Probability Vol. 28, Issue 3 (September 2015), 892–922
“Buffer-overflows: joint limit laws of undershoots and overshoots of reflected processes” (A. Mijatović and M. Pistorius), Stochastic Processes and their Applications Vol. 125, Issue 8 (August 2015), 2937– 2954
“Asymptotic independence of three statistics of maximal segmental scores” (A. Mijatović and M. Pistorius), Statistics & Probability Letters Vol. 99 (April 2015), 185–191
“Arbitrage-free prediction of the implied volatility smile” (P. Dellaportas and A. Mijatović), Risk Magazine, Technical Paper section, 30 April (2014)
“Markov Chain approximations for transition densities of Lévy processes” (A. Mijatović, M. Vidmar and S. D. Jacka), Electronic Journal of Probability Vol. 19 (2014), 1–37
“Mirror and synchronous couplings of geometric Brownian motions” (S. D. Jacka, A. Mijatović and D. Siraj), Stochastic Processes and their Applications Vol. 124, no. 2 (2014), 1055–1069
“Large deviations for the extended Heston model: the large-time case” (A. Jacquier and A. Mijatović), Asia-Pacific Financial Markets Vol. 21 (2014), 263–280
“Empirical asset pricing with non-linear risk premia” (A. Mijatović and P. Schneider), Journal of Financial Econometrics Vol. 12, no. 3 (2014), 479–506
“A note on delta hedging in markets with jumps” (A. Mijatović and M. Urusov), IMA Journal of Applied Mathematics Vol. 79, no. 2 (2014), 300–312
“Continuously monitored barrier options under Markov processes” (A. Mijatović and M. Pistorius), Mathematical Finance Vol. 23, no. 1 (2013), 1–38
“Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models” (A. Jacquier, M. Keller-Ressel and A. Mijatović), Stochastics Vol. 85, no. 2 (2013), 321–345
“Convergence of integral functionals of one-dimensional diffusions” (A. Mijatović and M. Urusov), Electronic Communications in Probability Vol. 17 (2012), 1–13
“On the limit distributions of continuous-state branching processes with immigration” (M. Keller-Ressel and A. Mijatović), Stochastic Processes and their Applications Vol. 122, no. 6 (2012), 2329–2345
“On the drawdown of completely asymmetric Lévy processes” (A. Mijatović and M. Pistorius), Stochastic Processes and their Applications Vol. 122, no. 11 (2012), 3812–3836
“Martingale property of generalized stochastic exponentials” (A. Mijatović, N. Novak and M. Urusov), Séminaire de Probabilités, XLIV, Lecture Notes in Mathematics Vol. 2046 (2012), 41–59
“Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models” (A. Mijatović and M. Urusov), Finance & Stochastics Vol. 16, no. 2 (2012), 225–247
“On the martingale property of certain local martingales” (A. Mijatović and M. Urusov), Probability Theory and Related Fields Vol. 152, no. 1 (2012), 1–30
“A note on essential smoothness in the Heston model” (M. Forde, A. Jacquier and A. Mijatović), Finance & Stochastics Vol. 15 (2011), 781–784
“A note on a paper by Wong and Heyde” (A. Mijatović and M. Urusov), Journal of Applied Probability Vol. 48, no. 3 (2011), 811–819
“Volatility derivatives in market models with jumps” (H. Lo and A. Mijatović), International Journal of Theoretical and Applied Finance Vol. 14, no. 07 (2011), 1159–1193
“Asymptotic formulae for implied volatility in the Heston model” (M. Forde , A. Jacquier and A. Mijatović), Proceedings of the Royal Society A Vol. 466, no. 2124 (2010), 3593–3620
“Approximating Lévy processes with a view to option pricing” (J. Crosby, N. Le Saux and A. Mijatović), International Journal of Theoretical and Applied Finance Vol. 13, Issue 1 (2010), 63–91
“Globally optimal parameter estimates for non-linear diffusions” (A. Mijatović and P. Schneider), Annals of Statistics Vol. 38, no. 1 (2010), 215–245
“Local time and the pricing of time-dependent barrier options” (A. Mijatović), Finance & Stochastics Vol. 14, Issue 1 (2009), 13–48
“Spectral properties of trinomial trees” (A. Mijatović), Proceedings of the Royal Society A Vol. 463, no. 2083 (2007), 1681–1696
“Spectral methods for volatility derivatives” (C. Albanese, H. Lo and A. Mijatović), Quantitative Finance Vol. 9, Issue 6 (2009), 663–692 arXiv:0905.2091
“A stochastic volatility model for risk-reversals in foreign exchange” (C. Albanese and A. Mijatović), International Journal of Theoretical and Applied Finance Vol. 12, Issue 6 (2009), 877–899
“Simplicial structures of knot-complements” (A. Mijatović), Mathematical Research Letters Vol. 12, no. 5-6 (2005), 843–856
“Triangulations of fibre-free Haken 3-manifolds” (A. Mijatović), Pacific Journal of Mathematics Vol. 219, no. 1 (2005), 139–186
“Triangulations of Seifert fibred manifolds” (A. Mijatović), Mathematische Annalen Vol. 330, no. 2 (2004), 235–273
“Simplifying triangulations of the 3-sphere” (A. Mijatović), Pacific Journal of Mathematics Vol. 208, no. 2 (2003), 291–324
Probability, Analysis and Number Theory: Papers in Honour of N. H. Bingham, Advances in Applied Probability Special Volume 48A, 2016 (co-edited by C.M. Goldie and A. Mijatović)
Spectral and Cubature Methods in Finance and Econometrics – special issue of International Journal of Theoretical and Applied Finance, 2011 (co-edited by S. Levendorskii, A. Mijatović and M. Pistorius)
"Reflecting random walks in curvilinear wedges" (M. V. Menshikov, A. Mijatović and A. R. Wade), In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, in Series Progress in Probability, Springer International Publishing (2021), Editors Maria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman, 637-675 arXiv:2001.06685
“Exotic derivatives in stochastic volatility models with jumps” (A. Mijatović and M. Pistorius), Advanced Mathematical Methods for Finance, Springer, 2011, Editors G. Di Nunno, B. Oksendal, 455–508, arXiv:0912.2595
“On additive time-changes of Feller processes” (A. Mijatović and M. Pistorius), Progress in Analysis and its Applications, Proceedings of the 7th International Isaac Congress, Imperial College London UK, 13 - 18 July 2009, 431–437, arXiv:0909.4881
"Martingale approach to control for general jump processes" (Ma. E. Hernández-Hernández, S. Jacka and A. Mijatović) arXiv:1912.13205.
"Invariance principles for local times in regenerative settings" (A. Mijatović and G. Uribe Bravo) arXiv:1910.09501.
“Coupling and a generalised Policy Iteration Algorithm in continuous time” (S. D. Jacka, A. Mijatović and D. Siraj) arXiv:1707.07834.
“Stationarity of entrance Markov chains and level-crossings of random walks” (A. Mijatović and V. Vysotskiy) arXiv:1808.05010.