Programme

Cyber insurance has become a key mechanism for managing the financial and operational consequences of cyber incidents in an increasingly digital economy. Cyber risk includes, but is not limited to, data breaches, ransomware, business email compromise, supply chain compromises, and cloud outages, and is characterized by rapidly evolving threats, strong interdependencies, heavy tailed losses, and limited reliable data. These features make cyber risk economically significant and statistically challenging. Cyber insurance provides first party and third-party coverage, yet the market remains volatile, with rising losses, tightening underwriting standards, and growing concern over correlated events. Systemic cyber risk, particularly cloud concentration and supply chain compromises, poses the greatest unresolved challenge and is increasingly the focus of regulators. The field offers rich opportunities to advance modelling and market design.

Modern organizations, irrespective of scale or sector, exhibit an escalating dependence on information and communication technology infrastructures and services. This systemic reliance inherently expands the organizational attack surface, precipitating a rise in cyber threats and necessitating robust security and privacy frameworks within cyberspace. To mitigate these risks, entities deploy an array of technical, organizational, human, and physical controls designed to reduce residual risk to levels aligned with institutional risk appetite. Concurrently, enterprises are incorporating cyber insurance into their core risk management strategies, leveraging it not only for risk transfer but also to enhance incident security management. In this context, the implementation of an Information Security Management System (ISMS) becomes critical. A structured ISMS facilitates standardized data and information exchange between the insured and the underwriter, thereby optimizing the underwriting process, enabling continuous security monitoring, and streamlining insurance claims management.

We propose a geometric framework for modeling and forecasting multi-asset markets. Projecting a 41-asset universe (2005–2025) onto its first three eigenportfolios, we ask whether the resulting trajectory evolves on a latent curved 2-manifold rather than in flat Euclidean space. Motivated by the uniformization theorem, we fit stochastic dynamics on the sphere, plane, hyperbolic plane, and torus, and infer the prevailing geometry through local Gaussian curvature estimation and sliding-window persistent homology. The evidence points consistently to torus-like structure: a two-loop topological signature appears in 88.4% of windows, which we interpret economically as two coupled macro-financial cycles arising from Hopf bifurcations in an IS–LM-type feedback system. Geometry-aware forecasts translate into economic value out of sample: an integrated geometry-informed model achieves a Sharpe ratio of 0.64 versus 0.44 for risk parity and 0.39 for long-only benchmarks, with gains surviving correlated-Brownian-motion null controls and non-linear learner comparisons. The results suggest that the structure PCA discards is not noise but organized curvature and cycles — and that respecting the market's shape improves predictions 

(Joint work with Professor A. N. Yannacopoulos)

Optimal switching problems arise in real options, energy markets, and stochastic control whenever an agent repeatedly changes operating regimes under uncertainty and at a cost. This presentation develops a unified computational pathway from structural reformulation to direct machine-learning solution. In a two-factor model driven by price and fast mean-reverting stochastic volatility, the original system of coupled quasi-variational inequalities is reduced to a single double-obstacle variational inequality for the difference between regime values. The reformulation preserves the switching regions while simplifying the finite-difference solution. Finite- difference parameter sweeps are also used to train supervised neural surrogates for the entry and exit boundaries, enabling rapid policy evaluation and sensitivity analysis. Although effective in low-dimensional settings, finite-difference methods become increasingly demanding as additional state variables and equations are introduced. The number of grid points required to represent the solution grows rapidly with the dimension of the state space, leading to substantially greater computational and memory requirements. This motivates the transition from grid-based numerical schemes to a physics-informed neural network that approximates the value difference directly, without relying on finite-difference labels. Training combines residuals from the governing partial differential equations (PDEs), the variational inequality, obstacles, boundary conditions, and smooth-pasting requirements, while residual-adaptive collocation concentrates training in numerically difficult regions. Alternative derivative-based boundary closures are assessed through matched finite-difference comparisons. The framework is finally extended to three factors by adding a mean-reverting state variable, turning switching curves into state-dependent entry and exit surfaces. The neural and finite-difference solutions recover consistent switching geometry, while independent residual tests provide additional validation where no analytical three-dimensional benchmark is available. Common-path simulations of complete discounted operating cycles further evaluate the economic consequences of the competing policies. Overall, the framework provides a flexible and scalable route from double-obstacle reduction and finite differences to the label-free neural solution of increasingly high-dimensional optimal switching problems.

(Joint work with Professor A. E. Tsekrekos and A. N. Yannacopoulos)

Measuring and managing the risks associated with artificial intelligence (AI) is increasingly critical as AI systems are integrated into high-stakes decision-making environments, such as healthcare. Algorithmic insurance offers a scalable financial solution for quantifying, pricing, and managing the risks inherent in AI deployment, complementary to regulation. It provides a structured mechanism for transferring the risks associated with AI systems from developers and users to insurers, creating a financial buffer that incentivizes responsible AI use and mitigates liability. Our work formalizes the concept of algorithmic insurance and proposes quantitative frameworks to estimate the risk exposure of insurance contracts for machine-driven financial risk. 

We study the effect of normalization on the layers of deep neural networks. A given layer with N hidden units is normalized by N^(-γ) with 1/2 < γ < 1. We study the effect of the choice of the γ on the statistical behavior of the neural network’s output (such as variance) as well as on the test accuracy and generalization properties of the architecture. We find that in terms of variance of the neural network’s output and test accuracy the best choice is to choose γ to be equal to one, which is the mean-field scaling. We also find that this is particularly true for the outer layer, in that the neural network’s behavior is more sensitive in the scaling of the outer layer as opposed to the scaling of the inner layers. The mechanism for the mathematical analysis is an asymptotic expansion for the neural network’s output. An important practical consequence of the analysis is that it provides a systematic and mathematically informed way to choose the learning rate hyperparameters. Such a choice guarantees that the neural network behaves in a statistically robust way as the number of hidden units N grow. Time permitting, applications of these ideas will be discussed to the design of deep learning algorithms for scientific problems including solving high dimensional partial differential equations (PDEs), closure of PDE models and reinforcement learning with applications to financial engineering, turbulence and more.

Monte Carlo simulation is a standard and universal method for computing intractable probabilities and expectations. However, it is impractical for probabilities of rare events, as a huge number of trials will be required to observe many instances of the event of interest. One way to resolve this problem is via importance sampling, i.e., sampling from a different distribution and reweighting the samples appropriately. A theoretical framework for the analysis of importance sampling algorithms was introduced in the classical work of Siegmund (1976). Motivated by the need to estimate the error rates of the sequential probability ratio test, Siegmund considered the problem of estimating the probability that a random walk with negative drift exits a bounded interval through the upper boundary. In this talk we will consider the more general problem of estimating the probability that a multi-dimensional random walk hits one of many unlikely convex regions before reaching an anticipated target. This problem arises naturally in the estimation of the error rates of many recent sequential multiple testing procedures. The work of Collamore (1996, 2002) suggests that a mixture distribution with a suitably designed component for each region achieves logarithmic efficiency, a weaker form of optimality than the one established by Siegmund in the one-dimensional case. However, this mixture becomes infeasible as the number of regions grows exponentially or even combinatorially with the dimension of the random walk, as is typically the case in the motivating statistical applications. For this reason, we will introduce a novel mixture distribution that preserves logarithmic efficiency but remains feasible as the number of regions increases. This distribution includes the optimal components only for some regions and combines them with additional proposals that control the variance across a large collection of regions.  We will illustrate this method in various concrete problems, including a multidimensional extension of Siegmund’s classical exit problem.

(Joint work with Professor Yanglei Song)

References:

• Siegmund, D. (1976) Importance sampling in the monte carlo study of sequential tests. The Annals of Statistics, 673–684.

• Collamore, JF. (1996) Hitting probabilities and large deviations. Ann. Probab.  24(4):2065–2078.

• Collamore, JF. (2002) Importance sampling techniques for the multidimensional ruin problem for general Markov additive sequences of random vectors. Ann. Appl. Probab.  12(1):382–421.

• Song, Y., & Fellouris, G. (2025). Efficient importance sampling for wrong exit probabilities over combinatorially many rare regions. arXiv preprint, arXiv:2509.14596

In this talk, we investigate the existence and uniqueness of Nash equilibria for a Mean Field Game (MFG) system subject to a possibly degenerate combination of idiosyncratic Brownian and jump-diffusion noises, within the framework of displacement monotonicity. We establish the existence of MFG equilibria through a classical Schauder fixed-point argument, without requiring any ellipticity assumptions or relying on (fractional) regularity estimates. We then turn to the uniqueness question, which is treated from a stochastic control perspective via the corresponding forward-backward stochastic differential equation (FBSDE) formulation. In particular, our results extend the existing well-posedness theory for displacement monotone MFG systems to models driven by Lévy–Itô jump diffusions, for potentially degenerate noise.

We revisit the problem of pricing perpetual American barrier-type options studied by Karatzas, I., & Wang, H. (2000). A barrier option of American type. Applied Mathematics & Optimization, 42(3), 259-279., this time with the additional assumption that the holder has the opportunity to exercise the option only at random epochs occurring according to an exogenous Poisson process with constant intensity. In contrast, the barrier-triggered deactivation of the option occurs under continuous monitoring e.g. by an automated system. By employing a constant optimal exercise boundary strategy and assuming geometric Brownian motion dynamics for the underlying asset price process, we provide closed form formulas for the expected present value of the options payoff, the probability of exercising the option and the Laplace transform of the time until exercising the option for both put and call option cases. The determination of the optimal exercise boundary and the fair price of the option is achieved by maximizing the option’s expected present value. The impact of the random exercise opportunities on the optimal expected present value, the optimal exercise threshold and the probability of the optimal exercise before the option is knocked-out is numerically investigated for the put and call option case.

(Joint work with Professor M. V. Boutsikas)

References:

• Dupuis, P., & Wang, H. (2002). Optimal stopping with random intervention times. Advances in Applied probability, 34(1), 141-157.

• Karatzas, I., & Wang, H. (2000). A barrier option of American type. Applied Mathematics & Optimization, 42(3), 259-279.

This talk presents a game-theoretic and learning-based framework for cyber-physical system security, with a focus on power-grid applications. The interaction between an attacker and a defender is modeled as a Stackelberg game and combined with Deep Reinforcement Learning using an Actor–Critic architecture. We consider both attacker-first and defender-first configurations and compare discrete-time and continuous-time formulations of the same security interaction. The two temporal models are evaluated in parallel under common scenarios and performance metrics, including system resilience, damage, response time, and learning stability. Simulation results show that both the leadership structure and the temporal formulation significantly affect system behavior. In particular, structured discrete-time decision making provides stable and effective proactive defense behavior, while continuous-time formulations reveal different trade-offs between response speed, system stability, and computational effort. The study highlights the potential of combining Stackelberg reasoning with adaptive learning for the design of dynamic CPS defense strategies. 

Artificial intelligence is increasingly used to process financial information, forecast risks, support investment decisions and automate trading. These applications promise greater efficiency, improved price discovery and more effective risk management. Finance, however, is a particularly challenging environment for AI: signals are weak, market regimes change, participants interact strategically, and predictions may themselves affect market outcomes. This lecture provides a non-technical overview of how machine learning and generative AI are reshaping financial decision-making and market dynamics. Particular attention is given to the transition from individual model risk to systemic risk: the widespread use of common data, models and technology providers may generate correlated strategies, crowded trades, liquidity pressures and procyclical behaviour. The lecture also discusses overfitting, model decay, hallucinations, explainability and the role of human oversight. Its central message is that AI does not eliminate financial uncertainty; it changes how information is processed, decisions are made and risk is transmitted through the financial system.

This study examines whether and how a target’s tone of textual information from annual reports (10-K filings) influences the subsequent mergers and acquisitions (M&A) bidders’ cumulative abnormal returns and takeover premiums. Using a sample of 620 U.S. bank M&As announced between 1996 and 2021, we find that the negative tone of 10-K filings is positively related to the announcement period abnormal returns and negatively related to the bid premium paid. This effect appears to be linked with the shareholders' positive perception of the success of the M&A when they buy the target at a lower price. Hence, our results indicate that acquirers make more profitable acquisition-investment decisions when the target firm’s financial statements exhibit a decline in terms of tone.

Neural Networks have introduced a new paradigm in the numerical approximation of solutions of PDEs and functions that represent important quantities in areas from physics to finance. In this talk, we will provide an overview of the construction of these Neural Networks, their training and testing, referring to topics such as Physics Informed Neural Networks and Structure Preserving Neural Networks. Examples from the field of credit risk modelling will be given based on relevant papers, which will provide an understanding of the modelling limitations and future important research directions.

Statistical process control charts for cryptocurrency market surveillance typically monitor a linear relationship between paired assets, such as Bitcoin (BTC) and Ethereum (ETH), through the daily intercept and slope of an ordinary least-squares fit. This linear representation cannot detect departures in which the BTC–ETH relationship changes shape rather than level or direction, since a curvature shift can be constructed to be nearly orthogonal to the linear basis it is compared against. We propose a hybrid monitoring scheme that combines a log linear baseline with a Gradient Boosting correction fitted to its residuals and monitors the resulting daily residual profile through four interpretable features: level, curvature, volatility, and asymmetry. Because tree-based learners cannot extrapolate beyond their training range, we further introduce a fade-out mechanism that returns predictions to the log linear baseline outside the training domain, together with a diagnostic flag identifying when this occurs and a limitation we find is not addressed by comparable machine-learning-based control charts in the literature. Using hourly BTC/ETH data  and a calibrated Monte Carlo simulation study across intercept, slope, variance, curvature, and asymmetry departures, we show the proposed chart is the only one of three compared procedures able to detect curvature, asymmetry, and variance shifts, while trading a modest reduction in sensitivity to pure linear shifts. The method identifies four verified signals in the real BTC/ETH series, two of which are curvature driven departures invisible to the linear benchmark.

(Joint work with Professor S. Psarakis)

Even though stochastic gradient descent (SGD) was fist introduced as a method for solving non-convex optimization problems more than 75 years ago, it remains the gold standard for training modern machine learning models and AI architectures. Still, despite the method's phenomenal success, we know surprisingly little about its long-run behavior—for example, which minimizers are more likely to be observed in the long run, or how long until it reaches a global minimum of the problem's objective function (if at all). In this talk, it will be outlined an approach to study the long-run behavior of SGD based on the theory of large deviations and randomly perturbed dynamical systems. Using this approach, we show that the limiting distribution of SGD follows the Boltzmann-Gibbs law of equilibrium thermodynamics with temperature equal to the method's step-size and energy levels determined by the problem's objective and the statistics of the noise. In particular, we show that, in the long run, (a) the iterates of SGD spend an exponentially small amount of time away from the problem's critical region; (b) any given critical point (or manifold thereof) is visited with probability that is exponentially proportional to its energy; (c) minimizers are visited exponentially more often than non-minimizers; and (d) SGD becomes exponentially concentrated around the problem's "ground state" (which does not always coincide with the minimum of the objective). It will also be provided a tight characterization of the global convergence time of SGD via matching upper and lower bounds which quantify the most “costly” set of obstacles that SGD may need to overcome to reach a global minimizer from a given initialization.

Weather may influence the financial performance of many industries, local government and households. It has been reported that weather impacts one third of the economy while weather effects may determine in the US a change in monthly employment data by more than 100,000 in either direction. Furthermore, uncertainty around climate legislation should be understood to be an increasingly important risk factor, with the potential to greatly affect government’s expenditure and decision-making, corporate profits and investors’ financial returns. Financial markets play several important roles in addressing climate change: (a) Provide information and important inputs for economic and policy decisions (mitigation, adaptation, monitoring), (b) Allocation of funds to sustainable investments and promoting technological transition (mitigation), (c) Managing and sharing climate risks (adaptation). The aim of this presentation is twofold. First, it presents a complete introduction to weather derivatives, weather risk management and the mechanics of the weather derivatives market. Second, it offers a complete financial engineering framework. It presents the designing, modelling and pricing of weather derivatives written on various underlying assets such as temperature, wind and precipitation.