Martin Larsson

About

Martin Larsson is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University, located in Wean Hall, Pittsburgh. His educational background includes a Ph.D. from Cornell University and a postdoctoral appointment at The Swiss Finance Institute at EPFL in Lausanne, Switzerland. His core research area is Mathematical Finance, with a focus on stochastic analysis and probability. His work centers on the theory and applications of finite- and infinite-dimensional affine and polynomial processes, stochastic convolution equations, and stochastic portfolio theory, among other topics. He has been recognized with awards such as the Bruti-Liberati Visiting Fellowship at the University of Technology Sydney.

Research topics

• Mathematics
• Applied mathematics
• Mathematical analysis

Selected publications

• A weak solution theory for stochastic Volterra equations of convolution type

  The Annals of Applied Probability · 2021 · 39 citations

  We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in Lp spaces. The main tools are new a priori estimates on Sobolev–Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit of…

  DOI

• Open markets and hybrid Jacobi processes

  The Annals of Applied Probability · 2024-06-01 · 4 citations

  articleSenior author

  We propose a unified approach to several problems in stochastic portfolio theory (SPT), which is a framework for equity markets with a large number d of stocks. Our approach combines open markets, where trading is confined to the top N capitalized stocks as well as the market portfolio consisting of all d assets, with a parametric family of models which we call hybrid Jacobi processes. We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these resul…

  PublisherDOI

• A composite generalization of Ville’s martingale theorem using e-processes

  Electronic Journal of Probability · 2023-01-01 · 4 citations

  articleOpen access

  We provide a composite version of Ville’s theorem that an event has zero measure if and only if there exists a nonnegative martingale which explodes to infinity when that event occurs. This is a classic result connecting measure-theoretic probability to the sequence-by-sequence game-theoretic probability, recently developed by Shafer and Vovk. Our extension of Ville’s result involves appropriate composite generalizations of nonnegative martingales and measure-zero events: these are respectively…

  PublisherDOI

• Sequential testing for elicitable functionals via supermartingales

  Bernoulli · 2024-02-01 · 3 citations

  articleOpen access

  We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal building blocks for constructing nonnegative supermartingales under the null. This in turn yields sequential tests via Ville’s inequality. Using regret bounds from Online Convex Optimization, we obtain rigorous guarantees on the asymptotic power of the tests for a wi…

  PublisherOA PDFDOI

• Minimum curvature flow and martingale exit times

  Electronic Journal of Probability · 2024-01-01 · 2 citations

  articleOpen access1st authorCorresponding

  We study the following question: What is the largest deterministic amount of time T∗ that a suitably normalized martingale X can be kept inside a convex body K in R d ? We show, in a viscosity framework, that T∗ equals the time it takes for the relative boundary of K to reach X(0) as it undergoes a geometric flow that we call (positive) minimum curvature flow. This result has close links to the literature on stochastic and game representations of geometric flows. Moreover, the minimum curvature…

  PublisherDOI

Recent grants

• High-Dimensional Open Markets and Long-Term Investing

  NSF · $300k · 2022–2026

Frequent coauthors

• Sergio Pulido

  Université d'Évry Val-d'Essonne

  61 shared

• Damir Filipović

  52 shared

• Johannes Ruf

  26 shared

• Robert A. Jarrow

  Cornell University

  19 shared

• Christa Cuchiero

  15 shared

• Martin Keller‐Ressel

  14 shared

• Sara Svaluto‐Ferro

  University of Verona

  14 shared

• Anders B. Trolle

  14 shared

Education

• Ph.D.

  Cornell University

Awards & honors

• Bruti-Liberati Visiting Fellowship (University of Technology…

Similar researchers at Carnegie Mellon University

• Alan Friezeh-74
• Michael Youngh-57
• David Kinderlehrerh-45