Department of Mathematics

Kakutani’s walk on spheres (WoS) has proven to improve the efficiency of Feynman-Kac formula in solving linear elliptic equations with constant coefficients in bounded domains where the geometry is ... More

We derive the short-maturity asymptotics for Asian option prices in local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large... More

I will start by introducing a general model for multi-agent stochastic control systems. We will observe the modeling power of these systems, as well as the optimality challenges that arise from asymme... More

In this talk, we will focus on operator learning, starting with a fundamental challenge of neural operators: how to mathematically approximate an operator. Mathematical insights provide a foundation f... More

Recession risk fluctuates ``before the storm'' of a recession. Incorporating this into a model of liquidity and investment allows firms to endogenously delay actions until recession risk increases. Wh... More

Kakutani’s walk on spheres (WoS) has proven to improve the efficiency of Feynman-Kac formula in solving linear elliptic equations with constant coefficients in bounded domains where the geometry is ... More

Although rough paths theory is typically applied to differential equations driven by stochastic processes, it is not inherently a random theory. Weierstrass functions are examples of Hölder continuo... More

[NOTE special Tuesday meeting]

I will discuss recent results that identify and correct bias in high dimensional eigenvectors. These results rely on geometry and concentration of measure in hig... More

An informal Q&A about mathematicians employed as quants in the financial sector. Dr. Goldberg has extensive experience mentoring in the investments world. All interested students are welcome to join ... More

There have been several prior works that study algorithmic stability and generalization error of heavy-tailed SGD such as Raj, Barsbey, Gürbüzbalaban, Zhu, ÅžimÅŸekli (ALT 2023) and Raj, Zhu, GürbÃ... More

This talk explores a comprehensive framework for solving stochastic control problems with noisy and or partial observations by integrating optimal filtering techniques. The study begins with modeling ... More

In most of today's electronic liquid markets (stocks, futures, foreign exchange), a continuous-time double auction procedure is carried out using a structure called the limit order book (LOB) in which... More