Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Microstructural Foundation of Rough Log-Normal Volatility Models

We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long lasting impact on volatility. Using a recently established C-t

Lab Rats Math 9.2 Rigor 2.5 ·  March 13, 2026

Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according to a Hawkes process with power-law kernel. After suitable r

Lab Rats Math 9.5 Rigor 2 ·  December 14, 2023

Path-dependent Fractional Volterra Equations and the Microstructure of Rough Volatility Models driven by Poisson Random Measures

We consider a microstructure foundation for rough volatility models driven by Poisson random measures. In our model the volatility is driven by self-exciting arrivals of market orders as well as self-exciting arrivals of limit orders and cancellations. The impact of market order on future order arri

Lab Rats Math 9 Rigor 2 ·  December 21, 2024

Extended mean-field games with multi-dimensional singular controls and non-linear jump impact

We establish a probabilistic framework for analysing extended mean-field games with multi-dimensional singular controls and state-dependent jump dynamics and costs. Two key challenges arise when analysing such games: the state dynamics may not depend continuously on the control and the reward functi

Lab Rats Math 9.5 Rigor 1.5 ·  February 14, 2024

Functional Limit Theorems for Hawkes Processes

We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and FCLTs under minimal conditions on the kernel of the process with the precise form of the limit theorems depending stron

Lab Rats Math 9.5 Rigor 1.5 ·  January 21, 2024

Mean-field control problems with multi-dimensional singular controls

We consider extended mean-field control problems with multi-dimensional singular controls. A key challenge when analysing singular controls are jump costs. When controls are one-dimensional, jump costs are most naturally computed by linear interpolation. When the controls are multi-dimensional the s

Lab Rats Math 9.5 Rigor 1.5 ·  August 8, 2023

A Mean-Field Game of Market Entry: Portfolio Liquidation with Trading Constraints

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while players with an initially long position are only allowed to sell

Lab Rats Math 9.2 Rigor 1.5 ·  March 15, 2024

Mean Field Portfolio Games with Epstein-Zin Preferences

We study mean field portfolio games under Epstein-Zin preferences, which naturally encompass the classical time-additive power utility as a special case. In a general non-Markovian framework, we establish a uniqueness result by proving a one-to-one correspondence between Nash equilibria and the solu

Lab Rats Math 9 Rigor 1.5 ·  May 12, 2025

Mean-Field Liquidation Games with Market Drop-out

We consider a novel class of portfolio liquidation games with market drop-out (“absorption”). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular round-trips are not admissible. This can be viewe

Lab Rats Math 9 Rigor 1.5 ·  March 10, 2023

Mean-field games with unbounded controls: a weak formulation approach to global solutions

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach doe

Lab Rats Math 9.5 Rigor 1 ·  March 5, 2026

Second-Order Approximation of Limit Order Books in a Single-Scale Regime

We establish a first and second-order approximation for an infinite dimensional limit order book model (LOB) in a single (‘‘critical’’) scaling regime where market and limit orders arrive at a common time scale. With our choice of scaling we obtain non-degenerate first-order and second-order approxi

Philosophers ·  August 1, 2023

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