Week 24.11.2025 – 30.11.2025

In this paper, we present a data-driven ensemble approach for option price prediction whose derivation is based on the no-arbitrage theory of option pricing. Using the theoretical treatment, we derive a common representation space for achieving domain adaptation. The success of an implementation of this idea is shown using some real data. Then we report several experimental results for critically examining the performance of the derived pricing models. This is a joint work with Dr. Anindya Goswami (IISER Pune, India)

The London Mathematical Society, which leads the Campaign for the Mathematical Sciences, recently put up a fund to encourage innovation in maths degrees with the goal of increasing the number of students who take up degrees in the mathematical sciences. King's College London were one of five universities awarded funding and will launch a new degree programme BSc Quantitative Mathematics in September 2027. In this talk I will provide further context about the state of mathematical science degrees in the UK, outline what our new degree programme is about and how it differs from KCL's existing programmes in the mathematical sciences, and share what I know about other four bid winners' plans.

In holographic CFT's, such as N=4 SYM, it is natural to organise the spectrum in single and multi particle states. By now we have a wealth of information about 4-point correlators with BPS single particle states, but much less is known about 4-point correlators involving multi particle states. I will discuss how we can calculate such correlators at strong coupling by using various techniques: bootstrap, OPE's of higher point functions and a bulk approach based on 1/2-BPS asymptotically AdS supergravity solutions. I will provide explicit results for various families of 4-point correlators with one or two 1/2-BPS multi particle states in the context of the AdS5/N=4 SYM duality.

Multivariate Markov Chain (MMC) models provide a powerful framework for
capturing dependencies among multiple interrelated processes that evolve
over time. They are widely used in finance, epidemiology, and genetics,
where understanding the joint behaviour of several variables is crucial
for prediction, risk assessment, and decision-making.

When all chains share the same discrete state space, a natural
parameterisation is through the joint transition probability matrix on
the extended state space formed by the Cartesian product of the marginal
spaces. However, the number of parameters grows rapidly with both the
number of states and the number of chains, creating major challenges for
estimation and inference.

In this talk, I will introduce alternative, general parameterisations
for MMC models that efficiently capture and characterise first-order
dependence between chains—such as conditional independence,
contemporaneous dependence, and Granger non-causality—while remaining
compatible with likelihood-based inference. I will also present a new
algorithm, the Generalized Individual Forward–Backward (GIFB) algorithm,
which provides exact (in a Monte Carlo sense) inference for latent
states in Hidden MMCs and reduces computational complexity from
exponential to quadratic in the number of chains.

The work is motivated by applications to multivariate Markov-modulated
Poisson processes for detecting disruption on the National Rail network
in Great Britain, using Twitter/X volume and content related to delays
and disturbances. If time permits, I will illustrate how the proposed
parameterisations can be applied to answer practically important
questions in this context.

With a convertible bond, in addition to coupon payments, the bondholder has the right to convert a bond into shares. Meanwhile, if the coupon payments become too expensive the shareholders have the right to end payments by declaring bankruptcy. This makes the convertible bond problem an archetypal non-zero sum Dynkin game. Often in non-zero sum Dynkin games it is assumed that each player would prefer that if the game is stopped, then stopping was done by the opponent. We consider games outside this paradigm, and what it means for the optimal strategies for the players. Joint work with Edward Wang and Gechun Liang

We analyze the effect of regulatory capital constraints on financial stability in a large homogeneous banking system using a mean-field game (MFG) model. Each bank holds cash and a tradable risky asset. Banks choose absolutely continuous trading rates in order to maximize expected terminal equity, with trades subject to transaction costs. Capital regulation requires equity to exceed a fixed multiple of the position in the tradable asset; breaches trigger forced liquidation. The asset drift depends on changes in average asset holdings across banks, so aggregate deleveraging creates contagion effects, leading to an MFG. We discuss the coupled forward–backward PDE system characterizing equilibria of the MFG, and we solve the constrained MFG numerically. Experiments demonstrate that capital constraints accelerate deleveraging and limit risk-bearing capacity. In some regimes, simultaneous breaches trigger liquidation cascades.

The last part of the presentation is devoted to the mathematical analysis of a model with time-smoothed contagion as in, e.g., Hambly, Ledger and Sojmark (2019) or Campi and Burzoni (2024). We characterize optimal strategies for a given evolution of the system and establish the existence of an MFG equilibrium.