Research

Preprints

• "Central limit theorem for superdiffusive reflected Brownian motion" (with I. Sauzedde and A. Wade) Youtube, arXiv

• "Asymptotically optimal Wasserstein couplings for the small-time stable domain of attraction" (with J. González Cázares and David Kramer-Bang) Youtube, arXiv:2411.03609

• "Limit Theorems for Stochastic Gradient Descent with Infinite Variance" (with Jose Blanchet and Wenhao Yang) arXiv:2410.16340

• "Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat" (with M. Brešar) YouTube: Part 1: tempared Langevin diffusions & Part 2: general results, arXiv:2408.13799

• "Superdiffusive limits for Bessel-driven stochastic kinetics" (with M. Brešar, C. da Costa and A.R. Wade) YouTube, arXiv:2401.11863

• "Modeling of Measurement Error in Financial Returns Data" (with A. Jasra and M. Maama) arXiv:2408.07405

• "Stationary entrance chains and applications to random walks" (with V. Vysotskiy) arXiv:2403.00619

• "Fast exact simulation of the first-passage event of a subordinator" (with J. González Cázares and F. Lin) YouTube, arXiv:2306.06927, GitHub Python and Julia implementation

Publications  

• "Subexponential lower bounds for f-ergodic Markov processes" (with M. Brešar), to appear in Probability Theory and Related Fields (2024), 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" (with J. González Cázares and F. Lin), to appear in Stochastic Systems (2024), 51 pp., YouTube, arXiv:2303.11964 , GitHub with implementation in Python and Julia  

• "Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability" (with M. Brešar and A.R. Wade), to appear in Annals of Probability (2024), 55 pp.,  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" (with R. Palfray) Applied Mathematical Finance (2024), 1–51pp. arXiv:2211.02528

• "When is the convex hull of a Lévy path smooth?" (with D. Bang and J. I. Gonzáles Cázares) Annales de l’Institut Henri Poincaré - Probabilités et Statistiques  Vol.  60, No 4 (2024) 2352–2381,  YouTube, arXiv:2205.14416.

• "Optimal Markovian coupling for finite activity Lévy processes" (with W.S. Kendall and M. B. Majka), Bernoulli, 30(4): 2821-2845 (2024) arXiv:2210.11251

• "How smooth can the convex hull of a Lévy path be?" (with D. Bang and J. I. Gonzáles Cázares), Electronic Journal of Probability, 29: 1-36 (2024), YouTube, arXiv:2206.09928.

• "Hölder continuity of the convex minorant of a Lévy process" (with D. Bang and J. I. Gonzáles Cázares), Electronic Communications in Probability, 28: 1-12 (2023), YouTube, arXiv:2206.12433.

• "Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity" (with M. V. Menshikov 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" (with J. I. Gonzáles Cázares and A. Kohatsu Higa), Bernoulli 29(4), 3443-3469 (2023) YouTube, arXiv:2008.01894.

• "Monte Carlo algorithm for the extrema of tempered stable processes" (with J. I. Gonzáles Cázares), 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" (with J. I. Gonzáles Cázares), Finance & Stochastics, Vol. 26 (2022), 671–732 YouTube, arXiv:2011.06618.

• "Asymptotic shape of the concave majorant of a Lévy process" (with D. Bang and J. I. Gonzáles Cázares), Annales Henri Lebesgue, Vol. 5 (2022), 779-811 YouTube, arXiv:2106.09066.

• "Limit theorems for local times and applications to SDEs with jumps" (with 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" (with J. I. Gonzáles Cázares), ALEA, Lat. Am. J. Probab. Math. Stat., 19, 983–999 (2022) YouTube, arXiv:2105.15060.

• “Geometrically Convergent Simulation of the Extrema of Lévy Processes” (with J. I. Gonzáles Cázares and G. Uribe Bravo), Mathematics of Operations Research 47(2):1141-1168, (2021) YouTube, arXiv:1810.11039.

• "A Gaussian approximation theorem for Lévy processes" (with D. Bang and J. I. Gonzáles Cázares), Statistics & Probability Letters, Vol. 178 (Nov 2021), arXiv:2104.13855.

• "Monte Carlo estimation of the solution of fractional partial differential equations" (with V. Kolokoltsov and F. Lin), Fractional Calculus and Applied Analysis, Vol. 24, no. 1, 278-306 (2021), arXiv:2012.13904.

• "Lévy processes on smooth manifolds with a connection" (with V. Mramor), Electronic Journal of Probability, 26: 1-39 (2021), YouTube, arXiv:2012.11633.

• "An algorithm for simulating Brownian increments on a sphere" (with 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” (with 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" (with J. I. Gonzáles Cázares 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” (with 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” (with M. Majka 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” (with J. I. Gonzáles Cázares 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” (with J. Vogrinc), Advances in Applied Probability, 51(4), 994-1026 (2019) arXiv:1707.08510.

• “Invariance principle for non-homogeneous random walks” (with N. Georgiou and A. Wade), Electronic Journal of Probability, 24:1-38 (2019) arxiv:1801.07882

• “Projections of spherical Brownian motion” (with 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” (with J. Vogrinc), Bernoulli Vol. 24, no. 3 (2018), 2401–2428

• “A radial invariance principle for non-homogeneous random walks” (with N. Georgiou and A. Wade), Electronic Communications in Probability Vol. 23 (2018), 11 pp.

• “Procuring load curtailment from local customers under uncertainty” (with 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" (with N. Georgiou, M. Menshikov 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” (with M. Pistorius), Electronic Communications in Probability Vol. 21 (2016), 1–18

• “Brownian manifolds, negative type and geo-temporal covariances” (with N. H. Bingham 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” (with 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” (with P. Gassiat and H. Oberhauser), Annals of Applied Probability Vol. 25, no. 4 (2015), 2039–2065

• “Coupling and tracking of regime-switching martingales ” (with S. D. Jacka), Electronic Journal of Probability Vol. 20 (2015), 39pp.

• “Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications” (with 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” (with 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” (with 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” (with M. Pistorius), Stochastic Processes and their Applications Vol. 125, Issue 8 (August 2015), 2937– 2954

• “Asymptotic independence of three statistics of maximal segmental scores” (with M. Pistorius), Statistics & Probability Letters Vol. 99 (April 2015), 185–191

• “Arbitrage-free prediction of the implied volatility smile” (with P. Dellaportas), Risk Magazine, Technical Paper section, 30 April (2014)

• “Markov Chain approximations for transition densities of Lévy processes” (with M. Vidmar and S. D. Jacka), Electronic Journal of Probability Vol. 19 (2014), 1–37

• “Mirror and synchronous couplings of geometric Brownian motions” (with S. D. Jacka 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” (with A. Jacquier), Asia-Pacific Financial Markets Vol. 21 (2014), 263–280

• “Empirical asset pricing with non-linear risk premia” (with P. Schneider), Journal of Financial Econometrics Vol. 12, no. 3 (2014), 479–506

• “A note on delta hedging in markets with jumps” (with M. Urusov), IMA Journal of Applied Mathematics Vol. 79, no. 2 (2014), 300–312

• “Continuously monitored barrier options under Markov processes” (with M. Pistorius), Mathematical Finance Vol. 23, no. 1 (2013), 1–38

• “Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models” (with A. Jacquier and M. Keller-Ressel), Stochastics Vol. 85, no. 2 (2013), 321–345

• “Convergence of integral functionals of one-dimensional diffusions” (with M. Urusov), Electronic Communications in Probability Vol. 17 (2012), 1–13

• “On the limit distributions of continuous-state branching processes with immigration” (with M. Keller-Ressel), Stochastic Processes and their Applications Vol. 122, no. 6 (2012), 2329–2345

• “On the drawdown of completely asymmetric Lévy processes” (with M. Pistorius), Stochastic Processes and their Applications Vol. 122, no. 11 (2012), 3812–3836

• “Martingale property of generalized stochastic exponentials” (with 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” (with M. Urusov), Finance & Stochastics Vol. 16, no. 2 (2012), 225–247

• “On the martingale property of certain local martingales” (with M. Urusov), Probability Theory and Related Fields Vol. 152, no. 1 (2012), 1–30

• “A note on essential smoothness in the Heston model” (with M. Forde and A. Jacquier), Finance & Stochastics Vol. 15 (2011), 781–784

• “A note on a paper by Wong and Heyde” (with M. Urusov), Journal of Applied Probability Vol. 48, no. 3 (2011), 811–819

• “Volatility derivatives in market models with jumps” (with H. Lo), International Journal of Theoretical and Applied Finance Vol. 14, no. 07 (2011), 1159–1193

• “Asymptotic formulae for implied volatility in the Heston model” (with M. Forde and A. Jacquier), Proceedings of the Royal Society A Vol. 466, no. 2124 (2010), 3593–3620

• “Approximating Lévy processes with a view to option pricing” (with J. Crosby and N. Le Saux), International Journal of Theoretical and Applied Finance Vol. 13, Issue 1 (2010), 63–91 

• “Globally optimal parameter estimates for non-linear diffusions” (with P. Schneider), Annals of Statistics Vol. 38, no. 1 (2010), 215–245

• “Local time and the pricing of time-dependent barrier options”, Finance & Stochastics Vol. 14, Issue 1 (2009), 13–48

• “Spectral properties of trinomial trees”, Proceedings of the Royal Society A Vol. 463, no. 2083 (2007), 1681–1696

• “Spectral methods for volatility derivatives” (with C. Albanese, H. Lo), Quantitative Finance Vol. 9, Issue 6 (2009), 663–692 arXiv:0905.2091

• “A stochastic volatility model for risk-reversals in foreign exchange” (with C. Albanese), International Journal of Theoretical and Applied Finance Vol. 12, Issue 6 (2009), 877–899

• “Simplicial structures of knot-complements”, Mathematical Research Letters Vol. 12, no. 5-6 (2005), 843–856

• “Triangulations of fibre-free Haken 3-manifolds”, Pacific Journal of Mathematics Vol. 219, no. 1 (2005), 139–186

• “Triangulations of Seifert fibred manifolds”, Mathematische Annalen Vol. 330, no. 2 (2004), 235–273

• “Simplifying triangulations of the 3-sphere”, Pacific Journal of Mathematics Vol. 208, no. 2 (2003), 291–324

Edited volumes

• Probability, Analysis and Number Theory: Papers in Honour of N. H. Bingham, Advances in Applied Probability Special Volume 48A, 2016 (co-edited with C.M. Goldie)

• Spectral and Cubature Methods in Finance and Econometrics – special issue of International Journal of Theoretical and Applied Finance, 2011 (co-edited with S. Levendorskii and M. Pistorius)

Book chapters

• "Reflecting random walks in curvilinear wedges" (with M. V. Menshikov 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” (with M. Pistorius), Advanced Mathematical Methods for Finance, Springer, 2011, Editors G. Di Nunno, B. Oksendal, 455–508,  arXiv:0912.2595

Conference proceedings

• “On additive time-changes of Feller processes” (with 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

Manuscripts

• "Martingale approach to control for general jump processes" (with Ma. E. Hernández-Hernández and S. Jacka)  arXiv:1912.13205.

• "Invariance principles for local times in regenerative settings" (with G. Uribe Bravo) arXiv:1910.09501.

• “Coupling and a generalised Policy Iteration Algorithm in continuous time” (with S. D. Jacka and D. Siraj) arXiv:1707.07834.

• “Stationarity of entrance Markov chains and level-crossings of random walks” (with V. Vysotskiy) arXiv:1808.05010.