Research

My research lies at the interface of probability theory, stochastic processes, and applied analysis, with a growing emphasis on foundational questions rather than applications. A central theme is the study of boundary-crossing and exit phenomena: how stochastic paths interact with fixed, moving, or random boundaries, how first-passage events decompose at the pathwise level, and how these events connect to the structure of random times, weak convergence, and compensators. Recent work develops a fine analysis of first-passage through continuous barriers for càdlàg processes, establishes continuity and limit results for exit times from time-dependent random domains, and studies reflected diffusions through excursion theory, including cumulative-load and extreme-burst statistics below a threshold.

Another recent direction moves toward geometric and topological probability. In particular, the work on Wiener sausages studies the multiscale topological complexity of Brownian paths through persistent homology, proving sampling-stability results, a law of large numbers and a central limit theorem for persistence functionals in the drifted planar case. This research program is being extended to the recurrent planar case of Brownian motion without drift. This contributes to a broader shift in my research toward structural questions about path geometry, asymptotic behavior, and the probabilistic content of topological observables.

Earlier in my career, much of my work was motivated by mathematical finance, but even there the mathematical core was already centered on boundary crossing, first-exit problems, PDE methods, and multivariate distributional analysis. This includes work on survival probabilities for Brownian motion under piecewise barriers, stochastic barriers, multidimensional Black–Scholes equations, and default-sensitive or vulnerable claims. So, even when the applications were financial, the underlying agenda was to obtain explicit analytical control of diffusion, jump, and boundary phenomena. Seen over time, the trajectory is from analytical methods for path-dependent valuation toward a more general probabilistic study of thresholds, path structure, and stochastic geometry.

Preprints

[31] Persistent Homology of the Wiener Sausage II: A Central Limit Theorem for Drifted Planar Brownian Motion

Link: https://arxiv.org/abs/2604.20327

[30] Persistence of the Wiener Sausage: Sampling Stability and a Law of Large Numbers for Drifted Planar Brownian Motion

Under review at Electronic Journal of Probability

Link: https://arxiv.org/abs/2604.03130

Seminar figures: https://drive.google.com/file/d/1fJwHdIq4KCoenLTZcZ9rVurUoiVD_4MB/view?usp=sharing

[29] First Passage through a Continuous Barrier: Pathwise Decomposition, Random-Time Structure, and Compensators

Under review at Advances in Applied Probability

Link: https://arxiv.org/abs/2604.03125

[28] Exit times from time-dependent random domains: continuity, weak convergence, and exit-time profiles

Under review at Stochastic Processes and their Applications.

Link: https://arxiv.org/abs/2604.03129

[27] Extrema, Barrier Options, and Semi-Analytic Leverage Corrections in Stochastic-Clock Volatility Models

Under review at Quantitative Finance

Link: https://hal.science/hal-05598087

Selection of articles published in peer-reviewed research journals

[26] Boundary Non-Crossing Probabilities as Functionals of the Deterministic Variance Clock

Axioms, 2026, 15 (5), 321

Link: https://doi.org/10.3390/axioms15050321

[25] Excursion Laplace Exponents under Height Truncation

Mathematics, 2026, 14 (6), 1014

Link: https://doi.org/10.3390/math14061014

[24] Survival Probabilities for Correlated Drifted Brownian Motions via Exit from Simplicial Cones

AppliedMath, 2026, 6 (3), 45

Link: https://doi.org/10.3390/appliedmath6030045

[23] Less vulnerable valuation of vulnerable options

Annals of Operations Research, 2025

Link: https://doi.org/10.1007/s10479-025-06755-w

[22] Analytical valuation of a general form of barrier option with stochastic interest rate and jumps

Review of Derivatives Research, 2025

Link: https://doi.org/10.1007/s11147-025-09215-6

[21] Computation of the survival probability of Brownian motion with drift subject to an intermittent step barrier

AppliedMath, 2024 , 4(3)

Link: https://doi.org/10.3390/appliedmath4030058

[20] Rainbow step barrier options

Journal of Risk and Financial Management, 2024, 17 (8)

Link: https://doi.org/10.3390/jrfm17080356

[19] Multitouch options

Journal of Risk and Financial Management, 2023, 16 (6)

Link: https://doi.org/10.3390/jrfm16060300

[18] Closed form valuation of barrier options with stochastic barriers

Annals of Operations Research, 2022, vol. 313(2), 1021-1050

Link: https://drive.google.com/file/d/1ySHNAGzOo2OJs0xhVFHpetDaj9os7QAs/view?usp=sharing

[17] On the Telegrapher's equation with three space variables in non-rectangular coordinates

Journal of Applied Mathematics and Physics, 2020, 8 (5), 910-926

Link: https://drive.google.com/file/d/1qCZglKEwBdp07u5Pjef97NTV8ws6s9XG/view?usp=sharing

[16] On the Multidimensional Black-Scholes Partial Differential Equation

Annals of Operations Research, 2019, 281 (1-2), 229-251

Link: https://drive.google.com/file/d/1V-BZjqfzkr3yKGB-Om56w54rjmknHPwA/view?usp=sharing

[15] On the First Exit Time of Geometric Brownian Motion from stochastic exponential boundaries

International Journal of Applied and Computational Mathematics, 2018, 4 : 120, 1 - 23

Link: https://drive.google.com/file/d/1Mk-u8_94h7VvvjAmeVbcpC0C-qoAfdF9/view?usp=sharing

[14] Computation of the quadrivariate and pentavariate normal cumulative distribution functions

Communications in Statistics - Computation and Simulation, 2018, 47 (3), 839-851

Link: https://drive.google.com/file/d/1gxaCidSw9Mrf7vf0fc8k5-F-48krra8G/view?usp=sharing

[13] First Exit Time from a Corridor

International Journal of Applied Mathematics and Statistics, 2017, 56 (2), 64-80

Link: https://drive.google.com/file/d/1dI9Ck2ceB2C2n3KH6Z3WTDJD8YMJHkQY/view?usp=sharing

[12] An analytically tractable model for pricing multi-asset options with correlated jump-diffusion equity processes and a two-factor stochastic interest rate

Journal of Applied Mathematics, 2016, Article ID 8029750

Link: https://drive.google.com/file/d/1QhSmcO0nMyWOfMu0RRsZX03VBGcEH3Iu/view?usp=sharing

[11] Computation of the Survival Probability of Brownian Motion with Drift when the Absorbing Boundary is a Piecewise Affine or Piecewise Exponential Function of Time

International Journal of Statistics and Probability, 2016, 5 (4), 119-138

Link: https://drive.google.com/file/d/1SXLBKFl5Q7ttLTtAGgSreBexV-1___Wa/view?usp=sharing

[10] On the Computation of the Survival Probability of Brownian motion with Drift in a Closed Time Interval when the Absorbing Boundary is a Step Function

Journal of Probability and Statistics, 2015, article ID391681

Link: https://drive.google.com/file/d/16MniRBO7Ij7yvZrL9JgY85wMMvPYHAVa/view?usp=sharing

[9] Analytical Valuation of Autocallable Notes

International Journal of Financial Engineering, 2015, 2 (2), 1-23

Link: https://drive.google.com/file/d/15Xfqhqq1GjfrLtXFrZcPhG_GcaHXlkjl/view?usp=sharing

[8] Autocallable Structured Products

Journal of Derivatives, 2015, 22 (3), 73-95

Link: https://drive.google.com/file/d/1Psu_b7l1g6DZM5g69zUV3Ik2qMEWOKby/view?usp=sharing

[7] On the Probability of Hitting a Time-Dependent Boundary for a Geometric Brownian Motion with Time-Dependent Coefficients

Applied Mathematical Sciences, 2014, 20 (8), 989-1009

Link: https://drive.google.com/file/d/1JWrFMVSizh6LYUSXmLz8r5wu5Yxha0bT/view?usp=sharing

[6] A Few Insights into Cliquet Options