The Mathematical Finance seminar is held regularly during termtime.
Monday 9 February 2026, 16:00-16:30
Watson Building, B16
We study the cost of maintaining decentralised connectivity in large networks when links are costly and nodes may fail. Requiring that every pair of nodes is connected by $d$ short, internally disjoint paths, and node degrees are nearly balanced, we give an explicit construction (Hydra) which minimises the maximum degree up to a small additive gap and achieves the minimal asymptotic number of links. The resulting edge count scales on the order of $n\log n$, quantifying how decentralisation raises connectivity costs relative to hub-based designs.
Monday 9 February 2026, 16:30-17:00
Watson Building, B16
Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.
Monday 9 March 2026, 16:00-16:30
Watson Building, B16
We show how the robustness of gamma hedging can be understood without using rough-path theory. Instead, we use the concepts of p-th variation along a partition sequence and Taylor's theorem directly, rather than defining an integral and proving a version of Itô's lemma. The same approach allows classical results on delta-hedging to be proved without defining an integral and without the need to define the concept of self-financing in continuous time. We show that the approach can also be applied to barrier options and Asian options.
Monday 9 March 2026, 16:30-17:00
Watson Building, B16
This paper examines how digitalisation amplifies liquidity pressures on banks during periods of financial stress, emphasising the role of social media in triggering unprecedented outflows in both size and speed, as witnessed during the March 2023 banking turmoil. To address this issue, we introduce a game-theoretic model where depositors' decisions are shaped by common information sources and the exchange of sentiments through social media networks. Our framework connects the global games literature, where agents receive private signals in isolation, with the classical Diamond and Dybvig (1983) setting, characterised by perfect information, which arises as a limiting case under full network connectivity. We highlight the critical role of depositor concentration and behavioural correlation in determining the likelihood and timing of withdrawals. The model also introduces two novel measures, UncertRisk and CorrRisk, which quantify uncertainty and correlation risks in modern banking environments. Finally, we assess the effectiveness of various policy interventions aimed at addressing the vulnerabilities associated with digitalisation and modern depositor behaviour.
Monday 16 March 2026, 16:00-16:30
Watson Building, B16
We develop asset pricing models that incorporate both financial and non-financial characteristics. The former include financials, financial ratios, market capitalisation, and multiples. The latter include carbon emissions, biodiversity, and diversity, equity and inclusion (DEI). We refer to the prices of these characteristics as 'pricing bases', which represent the marginal rate of substitution between future non-pecuniary consumption and present pecuniary consumption. We show that the asset price is the weighted sum of these pricing bases. Conventional CAPM and multi-factor models are thus special cases of our models. Furthermore, each pricing basis can be interpreted as the return on a portfolio aligned with the characteristics the investor wishes to focus on. Therefore, our models help to understand the long-standing debate surrounding the performance of well-known factor investing strategies, such as investing in small, value, or green stocks. We also demonstrate how the performance of new pricing bases compares with that of traditional ones.
Monday 16 March 2026, 16:30-17:00
Watson Building, B16
Sequencing customer arrivals in appointment systems is widely recognized as crucial yet highly challenging. However, there remains a lack of comprehensive insights into the dynamics of appointment sequencing, with only a few structural findings available in the literature. As a result, many studies resort to the shortest expected processing time first rule (SEPT) or the smallest variance first rule (SVF) based on conjecture or optimality demonstrations under specific assumptions. The rationale behind the SEPT/SVF rule lies in the propagation effect, where delays in preceding services can propagate down the sequence, leading to longer waits and delays for subsequent customers. In this study, we unveil a previously unidentified caesura effect that suspends the propagation of waiting times, rendering the SEPT/SVF rule suboptimal in many scenarios. Our investigation focuses on an appointment-based queue comprising two customer classes with stochastically ordered excess times. We elucidate the structural characteristics of the optimal sequence and evaluate the impact of the caesura effect when minimising the expected total waiting time. Furthermore, we extend our analysis to a system in which customers have different no-show probabilities rather than excess times. These findings provide valuable insights into the dynamics of sequencing heterogeneous services, thereby facilitating the development of efficient algorithms or heuristic procedures.
Monday 27 April 2026, 15:30-16:00
Watson Building, B16
We consider a panel model for a large cross-section of equity options implied volatilities surfaces that depend on moneyness and time to maturity and whose dynamics are determined by common scalar factors. To reduce the dimensionality of the problem, we assume the response functions to the factors are representable through common fixed functional components and idiosyncratic scalar coefficients. We use the idiosyncratic coefficients to construct equity options portfolios that exploit the idea of 'beta-sorted portfolios' in the implied volatility space. The shape of each common component is informative for designing economically meaningful strategies that exploit volatility, skewness, and termstructure risk. We find significant alphas for the long-short portfolios. This is a joint work with P. Santucci de Magistris, A. Popa and F. Violante.
Monday 27 April 2026, 16:00-16:30
Watson Building, B16
We present some optimal stopping problems over the set of Bermudan-type strategies (which we understand in a more general sense than the stopping strategies for Bermudan options in finance) and with general doubly indexed non-linear operators (non-linear evaluations) assessing the rewards. We provide a characterization of the value family $V$ in terms of a suitably defined non-linear Snell envelope of the pay-off family. We establish a Dynamic Programming Principle. We provide an optimality criterion in terms of a non-linear martingale property of $V$ on a stochastic interval. If time permits, we will also present a non-linear multiple stopping problem and a non-linear non-zero-sum game problem in the above framework. The talk is based on recent works with Marie-Claire Quenez and Peng Yuan.
Monday 27 April 2026, 16:30-17:00
Watson Building, B16
We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of forward optimized certainty equivalent (forward OCE), which offers a genuinely dynamic valuation mechanism that accommodates progressively adaptive market model updates, stochastic risk preferences, and incoming claims with arbitrary maturities. In parallel, we develop a new methodology to analyze the emerging stochastic optimization problems by directly studying the candidate optimal control processes for both the primal and dual problems. Specifically, we derive two new systems of forward-backward stochastic differential equations (FBSDEs) and establish necessary and sufficient conditions for optimality, and various equivalences between the two problems. We provide representative examples for forward performance criteria with random endowment and forward OCE. For the case of exponential criteria, we investigate the connection between forward OCE and forward entropic risk measure. Based on joint work with Yifan Sun and Thaleia Zariphopoulou.
Monday 27 April 2026, 17:00-17:30
Watson Building, B16
We study a consumption-investment problem in a multi-asset market where the returns follow a generic rank-based model. Rank-based models prescribe drift and volatility dynamics for each asset according to the rank they occupy, rather than the company name, and have been widely studied in stochastic portfolio theory. Our main result derives an HJB equation with Neumann boundary conditions for the value function and proves a corresponding verification theorem. The control problem is nonstandard due to the discontinuous nature of the coefficients in rank-based models, requiring a bespoke approach of independent mathematical interest. The special case of first-order models, prescribing constant drift and diffusion coefficients for the ranked returns, admits explicit solutions when the investor is either (a) unconstrained, (b) abides by open market constraints or (c) is fully invested in the market. The explicit optimal strategies in all cases are related to the celebrated solution to Merton's problem, despite the intractability of constraint (b) in that setting.