Peter Carr Seminar Series: Abderrahmane Abbou & Andrey Itkin

Abderrahmane Abbou

Africa Business School (UM6P)

Title

Intervention Scheduling under Partial Information and Resource Limitation

Astract

The research formulates a restless bandit model for the optimal allocation of intervention resources under partial information. Applying optimal stopping theory, the research develops a simple index policy for assigning intervention priorities based on noisy data from randomly failing bandits, assuming each bandit’s data is generated by a Wiener process that gains drift due to the failure of the bandit. Moreover, the research derives a provable bound on the (unknown) optimal performance, enabling the optimality gap evaluation of the index policy. Numerical experiments demonstrate the near-optimal performance of the index policy. The effectiveness of the proposed methodology is illustrated in a real-world digital marketing application.

Bio

Abderrahmane ABBOU is an Assistant Professor at Africa Business School (UM6P). He holds a Ph.D. in Operations Research from the University of Toronto. His research focuses on the development of algorithms for sequential decision making under uncertainty and their applications to dynamic resource allocation. Abderrahmane worked as a risk modelling researcher at CIBC Capital Markets Risk Management and as a postdoctoral fellow at the University of Delaware.

Andrey Itkin

NYU Tandon Finance and Risk Engineering Department

Title

Semi-analytical pricing of American options via integral equations and the GIT method

Abstract

We present a semi-analytical approach for pricing American options, including assets paying discrete or continuous dividends. Our method leverages the Generalized Integral Transform (GIT), which reframes the pricing problem - traditionally a complex partial differential equation with a free boundary - as a Volterra integral equation of the first kind. For transparency, we assume the underlying asset follows a time-inhomogeneous Geometric Brownian Motion, though the approach has been already extended to various pure diffusion or jump-diffusion models. By solving this integral equation, we can efficiently determine both the option price and the early exercise boundary while naturally accommodating the discontinuities introduced by discrete dividends. This methodology offers a powerful alternative to standard numerical techniques like binomial trees or finite difference methods, which often struggle with the jump conditions from discrete dividends, leading to a loss of accuracy or performance. Several examples demonstrate that the GIT method is both highly accurate and computationally efficient, as it bypasses the need for extensive computational grids or complex backward induction.

Bio

Dr. Andrey Itkin is an Adjunct Professor in NYU's Department of Risk and Financial Engineering. With a PhD in the physics of liquids, gases, and plasma and a Doctor of Science in computational physics, he has authored several books and numerous publications spanning chemical physics, astrophysics, and computational and mathematical finance. Dr. Itkin has also held various research and managerial roles in the financial industry and is a member of several professional associations in finance and physics. He is also serving as Editor-in-Chief of the Review of Modern Quantitative Finance book series and on the Editorial Boards of the Journal of Derivatives and the International Journal of Computer Mathematics (2014-2024).