Research

My doctoral work develops a general MSPD framework for multivariate self-exciting point processes. The aim is to capture complex, event-driven interactions across multiple components (e.g. cyber events across entities, climate shocks across regions) while retaining analytical tractability. Using Malliavin calculus on Poisson spaces, I obtain expressions for expectations, covariances and, more generally, functionals of shifted MSPD paths. This allows me to compute sensitivities and scenario impacts in a way that is both mathematically rigorous and aligned with risk management practice.

In cyber risk, MSPDs provide a flexible tool to describe how incidents trigger further activity across time, business units, or entities. I am particularly interested in linking these dynamics to solvency constraints, loss distributions, and decision-relevant indicators. The interactive toy models presented on the home page are designed to communicate these ideas visually: one focuses on MSPD dynamics for cyber; the other highlights scenario-based stresses and shifted-path analysis, echoing the kind of "what-if" questions asked by boards and regulators.

A central theme of my research agenda is to connect advanced stochastic models with the constraints of real internal models and regulatory frameworks (e.g. Solvency II). Pseudo-chaotic decompositions and shifted-path operators offer explicit contributions of different event-types and scenarios, which can be translated into stress testing tools for practitioners. In future work, I plan to extend these methods to climate-related and longevity risks, and to explore computational strategies (e.g. simulation-based inference, variance reduction) to scale MSPD-based models to larger data sets.