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

• Markovian projections for functionals of Itô semimartingales with jumps

  Electronic Journal of Probability · 2026-01-01

  preprintOpen access1st authorCorresponding

  Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of $\widehat{X}$ but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~\cite{MR3098443}. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps.

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• Testing Hypotheses Generated by Constraints

  Mathematics of Operations Research · 2026-05-12

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  E-variables are nonnegative random variables with expected value at most one under any distribution from a given null hypothesis. Every nonasymptotically valid test can be obtained by thresholding some e-variable. As such, e-variables arise naturally in applications in statistics and operations research, and a key open problem is to characterize their form. We provide a complete solution to this problem for hypotheses generated by constraints—a broad and natural framework that encompasses many hypothesis classes occurring in practice. Our main result is an abstract representation theorem that describes all e-variables for any hypothesis defined by an arbitrary collection of measurable constraints. We instantiate this general theory for three important classes: hypotheses generated by finitely many constraints, one-sided sub-[Formula: see text] distributions (including sub-Gaussian distributions), and distributions constrained by group symmetries. In each case, we explicitly characterize all e-variables as well as all admissible e-variables. Numerous examples are treated, including constraints on moments, quantiles, and conditional value-at-risk (CVaR). Building on these, we prove the existence and uniqueness of optimal e-variables under a large class of expected utility-based objective functions used for optimal decision making, in particular covering all criteria studied in the e-variable literature to date. Funding: This research was supported by the National Science Foundation [Grants NSF DMS-2310718 and NSF DMS-2510965] and a Sloan Fellowship.

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• Optimal Contracts for Delegated Order Execution

  Mathematical Finance · 2025-04-23

  articleOpen access1st authorCorresponding

  ABSTRACT We determine the optimal affine contract for a client who delegates their order execution to a dealer. Existence and uniqueness are established for general linear price impact dynamics of the dealer's trades. Explicit solutions are available for the model of Obizhaeva and Wang, for example, and a simple gradient descent algorithm is applicable in general. The optimal contract allows the client to almost achieve the first‐best performance without any agency conflicts for many reasonable parameter values. Common trading arrangements arise as limiting cases. In particular, optimal contracts for many reasonable model parameters resemble the “fixing contract” common in FX markets, in that they only incorporate market prices briefly before the conclusion of the trade. Price manipulation by the dealer is avoided by only putting a sufficiently small weight on these prices, and complementing this part of the contract with a sufficiently large fixed fee.

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• Nonasymptotic and distribution-uniform Komlós-Major-Tusnády approximation

  ArXiv.org · 2025-02-10

  preprintOpen access

  We present nonasymptotic concentration inequalities for sums of independent and identically distributed random variables that yield asymptotic strong Gaussian approximations of Komlós, Major, and Tusnády (KMT) [1975,1976]. The constants appearing in our inequalities are either universal or explicit, and thus as corollaries, they imply distribution-uniform generalizations of the aforementioned KMT approximations. In particular, it is shown that uniform integrability of a random variable's $q^{\text{th}}$ moment is both necessary and sufficient for the KMT approximations to hold uniformly at the rate of $o(n^{1/q})$ for $q > 2$ and that having a uniformly lower bounded Sakhanenko parameter -- equivalently, a uniformly upper-bounded Bernstein parameter -- is both necessary and sufficient for the KMT approximations to hold uniformly at the rate of $O(\log n)$. Instantiating these uniform results for a single probability space yields the analogous results of KMT exactly.

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• Inverting the Markovian projection for pure jump processes

  Stochastic Processes and their Applications · 2025-10-18

  articleOpen access1st authorCorresponding
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• The fast rate of convergence of the smooth adapted Wasserstein distance

  ArXiv.org · 2025-03-13

  preprintOpen access1st authorCorresponding

  Estimating a $d$-dimensional distribution $μ$ by the empirical measure $\hatμ_n$ of its samples is an important task in probability theory, statistics and machine learning. It is well known that $\mathbb{E}[\mathcal{W}_p(\hatμ_n, μ)]\lesssim n^{-1/d}$ for $d>2p$, where $\mathcal{W}_p$ denotes the $p$-Wasserstein metric. An effective tool to combat this curse of dimensionality is the smooth Wasserstein distance $\mathcal{W}^{(σ)}_p$, which measures the distance between two probability measures after having convolved them with isotropic Gaussian noise $\mathcal{N}(0,σ^2\text{I})$. In this paper we apply this smoothing technique to the adapted Wasserstein distance. We show that the smooth adapted Wasserstein distance $\mathcal{A}\mathcal{W}_p^{(σ)}$ achieves the fast rate of convergence $\mathbb{E}[\mathcal{A}\mathcal{W}_p^{(σ)}(\hatμ_n, μ)]\lesssim n^{-1/2}$, if $μ$ is subgaussian. This result follows from the surprising fact, that any subgaussian measure $μ$ convolved with a Gaussian distribution has locally Lipschitz kernels.

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• Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction

  Journal of Theoretical Probability · 2024-12-20 · 1 citations

  articleOpen access

  Abstract We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean–Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics.

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• Martin Larsson, Aaditya Ramdas, and Johannes Ruf’s contribution to the Discussion of ‘Safe testing’ by Grünwald, de Heide, and Koolen

  Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2024-06-26

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• Markovian projections for Itô semimartingales with jumps

  arXiv (Cornell University) · 2024-03-24

  preprintOpen access1st authorCorresponding

  Given a general Itô semimartingale, its Markovian projection is an Itô process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for Itô semimartingales with jumps, whose flows of one-dimensional marginal laws are solutions to non-local Fokker--Planck--Kolmogorov equations (FPKEs). As an application, we show how Markovian projections appear in building calibrated diffusion/jump models with both local and stochastic features.

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• On concentration of the empirical measure for radial transport costs

  Stochastic Processes and their Applications · 2024-08-28 · 1 citations

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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…