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Christopher Blier-Wong, University of Toronto

Multi-view spatial embeddings for insurance

Accurate assessment of spatial risks, particularly those influenced by climate, weather, and demographic factors, is crucial for the insurance industry to improve underwriting precision and enhance risk management. This paper introduces a novel approach for constructing spatial embeddings using contrastive learning techniques in a multi-view setting. The proposed method generates embeddings that capture complex spatial features relevant to insurance risks. We develop and train a model leveraging these embeddings to analyze spatial risk distributions, with case studies demonstrating predictive accuracy, monitoring spatial changes over time, and evaluating the impact of climate change scenarios on portfolio risk. This study highlights the potential of advanced spatial embeddings and novel geographic data sources to improve risk assessment and decision-making processes within the insurance sector.

Anran Hu, Columbia University

Continuous-time mean field games: a primal-dual characterization

This talk presents a primal-dual formulation for continuous-time mean field games (MFGs) and establishes a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the representative player's control problem with {\it measurable coefficients} is equivalent to a linear program over the space of occupation measures. We then establish the dual formulation of this linear program as a maximization problem over smooth subsolutions of the associated Hamilton-Jacobi-Bellman (HJB) equation, which plays a fundamental role in characterizing NEs of MFGs. Finally, a complete characterization of \emph{all NEs for MFGs} is established by the strong duality between the linear program and its dual problem. This strong duality is obtained by studying the solvability of the dual problem, and in particular through analyzing the regularity of the associated HJB equation.

Coffee break

Zhiwei Tong, University of Iowa

Dependence Modeling in Climate-Related Losses: A Joint Frequency–Severity Framework and a Spatial Empirical Study

This presentation introduces two projects that explore dependence structures in climate-related risks. The first project proposes a SAFE (Sign-Aligned Frequency-Severity in Climate Extremes) model to jointly capture the frequency and severity of climate-induced losses. The SAFE model incorporates a sign-aligned regularization term that promotes consistent directional effects of covariates across the frequency and severity components. It is estimated using an alternating minimization algorithm with proximal gradient descent. Extensive simulations demonstrate the model’s superior predictive performance and stability. The second project investigates spatial dependence in crop insurance indemnities. The explanatory model is a panel regression that includes a proxy variable for climate patterns and controls for regional effects. The predictive model combines principal component analysis with standard time series methods. We find strong evidence that the proxy variable plays a significant role in aggregate losses distribution.

Emma Hubert, Princeton University

The seminal work of Cvitanic, Possamaï, and Touzi (2018) [1] introduced a general framework for continuous-time principal-agent problems using dynamic programming and second-order backward stochastic differential equations (2BSDEs). In this talk, we first propose an alternative formulation of the principal-agent problem that allows for a more direct resolution using standard BSDEs alone.

Our approach is motivated by a key observation in [1]: when the principal observes the output process continuously, she can compute its quadratic variation pathwise. While this information is incorporated into the contract in [1], we consider a reformulation where the principal directly controls this process in a ‘first-best’ setting. The resolution of this alternative problem follows the methodology known as Sannikov’s trick in continuous-time principal-agent problems, as originally introduced by Sannikov (2008). We then demonstrate that the solution to this ‘first-best’ formulation coincides with the original problem’s solution. More specifically, leveraging the contract form introduced in [1], we establish that the ‘first-best’ outcome can be attained even when the principal lacks direct control over the quadratic variation. Crucially, our approach does not require the use of 2BSDEs to prove contract optimality, as optimality naturally follows from achieving the ‘first-best’ scenario.

We believe that this reformulation offers a more accessible approach to solving continuous-time principal-agent problems with volatility control, facilitating broader dissemination across various fields. In the second part of the talk, we will explore how this methodology extends to more complex settings, particularly multi-agent frameworks.

Lunch break

Qiuqi Wang, Georgia State University

Backtesting risk measures is important for financial regulators to evaluate risk forecasts reported by financial institutions. As a natural extension to standard/traditional backtests, comparative backtests are introduced to compare different forecasting methods. Based on recently developed concepts of e-values and e-processes, we design a model-free method for standard backtests of identifiable risk measures. In addition, we develop model-free comparative backtests for elicitable risk measures by constructing e-processes. Our e-tests are applicable to a wide range of common risk measures including the mean, the variance, the Value-at-Risk, the Expected Shortfall, and the expectile. Our results are illustrated by extensive simulation studies and real data analysis.

Samuel Gyamerah, Toronto Metropolitan University

The stability of the financial system is one of the most important factors for economic growth and resilience. In the process of increasing globalization, the interconnectedness of financial institutions such as banks has increased considerably. Although this interdependence enhances economic efficiency, it exposes the financial system to systemic risks. Bank runs can destabilize individual institutions and, through financial networks, spread into general economic crises. The study explores the interconnection of systemic risk in the banking system, emphasizing interbank networks as the primary means of propagating financial contagion. We propose a compartmental system through which contagion is propagated. The system classifies the banks in the network into undistressed, exposed, distressed, liquid, run, and failed states. We investigate the existence of a risk-free equilibrium point (a state where no financial distress exists), an endemic equilibrium (a state where financial distress persists at a low but stable level), and local asymptotic stability (a state where minor financial shocks will not lead to widespread contagion) and conduct a sensitivity analysis of the system. We show the existence of different optimal control strategies (liquidity injections by the government, deposit insurance, and calming down depositors withdrawing their money).

Coffee break

Thibaut Mastrolia, University of California, Berkeley

Optimal Rebate Design: Incentives, Competition and Efficiency in Auction Markets

We study the design of an efficient rebate policy in auction markets, focusing on a continuous-time setting with competition among market participants. In this model, a stock exchange collects transaction fees from auction investors executing block trades to buy or sell a risky asset, then redistributes these fees as rebates to competing market makers submitting limit orders. Market makers influence both the price at which the asset trades and their arrival intensity in the auction. We frame this problem as a principal-multi-agents problem and provide necessary and sufficient conditions to characterize the Nash equilibrium among market makers. The exchange’s optimization problem is formulated as a high-dimensional Hamilton-Jacobi-Bellman equation with Poisson jump processes, which is solved using a verification result. To numerically compute the optimal rebate and transaction fee policies, we apply the Deep BSDE method. Our results show that optimal transaction fees and rebate structures improve market efficiency by narrowing the spread between the auction clearing price and the asset’s fundamental value, while ensuring a minimal gain for both market makers indexed on the asset price on a coexisting limit order book. Joint work with Tianrui Xu (UC Berkeley).

Klaus Herrmann, Université de Sherbrooke

In this talk we revisit minimization based univariate risk measures. Specifically, quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This leads to the formulation of a general class of statistical functionals which we call meanimiles. Meanimiles contain next to the above concepts many interesting quantities, including a subclass of distortion risks, as well as new concepts. The focus of this talk is to discuss theoretical properties of meanimiles, to present estimators for such functionals and to establish asymptotic consistency and asymptotic normality of these estimators. The advantage of the general framework is that it allows application to a very broad range of concepts, providing as such estimation tools and tools for statistical inference (for example for construction of confidence intervals) for all members of the class in one single effort. After developing the theory for the general functional we apply it to various settings, illustrating the broad applicability. Special attention is devoted to the case of the square loss function, where we establish a connection to distributionally distorted random variables. For this case we discuss the impact of distributional distortions on risk measures. As a last point we conduct simulation studies and discuss an application to the analysis of natural disasters.

This talk is based on joint work with Dieter Debrauwer (KU Leuven) and Irène Gijbels (KU Leuven).

Banquet dinner

Light refreshments

Johannes Wiesel, Carnegie Mellon University & University of Copenhagen

The Wasserstein distance Wp is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance AWp extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems.

While the topological differences between Wp and AWp are well understood, their differences as metrics remain largely unexplored beyond the trivial bound Wp≲AWp. This paper closes this gap by providing upper bounds of AWp in terms of Wp through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of Wp, Eder's modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on Wp automatically hold for AWp under mild regularity assumptions on the measures considered. 

Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter. 

This talk is based on joint work with Martin Larsson and Jonghwa Park.

Linfeng Zhang, The Ohio State University

Microdata sharing is a common practice that enables various parties to benefit from the analysis of fine-grained information. However, it also poses a serious threat to the privacy of the individuals whose data are shared, as malicious actors may attempt to infer their sensitive attributes or identities from the shared data. To protect the privacy of the data subjects, data controllers often apply privacy-preserving techniques that introduce some distortion or noise to the original data, making it harder for an adversary to link them to specific individuals. However, these techniques also reduce the utility and accuracy of the data for legitimate analysis purposes. Therefore, a key challenge for data controllers is balancing the trade-off between privacy loss and data utility when choosing a suitable privacy-preserving technique. In this paper, we revisit a previously proposed method that allows partial recovery of the utility of randomized microdata by exploiting some auxiliary information. Based on this method, we propose a decision-making process that helps data controllers select the optimal differential privacy mechanism that minimizes privacy loss while meeting the utility requirement.

Coffee break

Dominykas Norgilas, North Carolina State University

Suppose we are given the market prices of European put/call options. Naturally, any pricing model, that can be used to price other exotic derivatives, should be consistent with the market quotes of these vanilla claims. Among such models, can we identify those that minimize/maximize the no-arbitrage price of a Bermudan option? We study this problem with the help of optimal transport.

Tolulope Fadina, University of Illinois Urbana-Champaign

In this talk, we consider how an insurance company manages insurance contracts that relate to financial markets, such as equity-linked insurances or variable annuities. We introduce stochastic mortality, which is not necessarily independent from the financial market. This is a key feature of the recent Corona crisis: increasing mortality together with falling stock prices. We propose a model that is able to capture uncertain circumstances and compute the associated impact of the pandemic risk.

This is a joint work with Fangda Liu and Thorsten Schmidt.

Lunch

Dena Firoozi, HEC Montréal

Mean field games (MFGs) were originally developed in finite-dimensional spaces. However, there are scenarios where Euclidean spaces do not adequately capture the essence of problems such as those involving non-Markovian systems. We present a comprehensive study of linear-quadratic (LQ) MFGs in Hilbert spaces, involving agents whose dynamics are governed by infinite-dimensional stochastic equations. We first study the well-posedness of a system of N coupled semilinear stochastic evolution equations establishing the foundation of MFGs in Hilbert spaces. We then specialize to N-player LQ games and study the asymptotic behavior as the number of agents, N, approaches infinity. We develop an infinite-dimensional variant of the Nash Certainty Equivalence principle and characterize a unique Nash equilibrium for the limiting MFG. Furthermore, we demonstrate that the resulting limiting best-response strategies form an ϵ-Nash equilibrium for the N-player game in Hilbert spaces.

Siyang Tao, Ball State University

Direct valuation of variable annuity guarantees relies on nested simulation, which is computationally costly. One way of feasibly valuing large portfolios relies on a two-step process in which such computationally intensive valuations are only performed on a set of carefully chosen representative policies. These values are then used to train a predictive model to obtain those for the remainder of the portfolio. This is known as the metamodeling framework. We empirically demonstrate that, when used as the predictive model, neural networks outperform state-of-the-art tree-based methods in terms of valuation accuracy. Further, we introduce Neural Tangent Kernel (NTK) regression as an easier-to-use and better-performing alternative to standard neural networks. NTK regression is equivalent to fitting the corresponding neural network with layers of infinite width, sidestepping the need to specify the number of nodes. As a kernel regression method, it is also easier to optimize, simplifying greatly the tuning process. We demonstrate that, in the setting of variable annuity valuation, NTK regression delivers significantly better empirical performance compared to finite-width networks.

Coffee break

Zhenzhen Huang, The Ohio State University

Environmental, Social, and Governance (ESG) investing has emerged as a global trend, offering sustainable benefits to investors and financial institutions. This study integrates an ESG constraint into the classical mean-variance optimization framework, while accounting for the estimation risk associated with the first two moments of asset returns. We begin by examining the problem in the absence of estimation risk and deriving the optimal portfolio characterized by three-fund separation. To address estimation risk, we propose a combined three-fund portfolio, with components based on a plug-in ESG portfolio. The optimal combination coefficients are derived by maximizing the expected out-of-sample mean-variance utility. Furthermore, we provide a comparative performance analysis on the ESG-constrained portfolios involved in the study. Extensive simulations and empirical analysis demonstrate that the combined portfolio outperforms the plug-in ESG portfolio in terms of certainty equivalent return.

Max Reppen, Boston University

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. When small, a firm chooses to act early when risk is low to protect attractive investments as investment reduces cash and raises liquidation risk. A larger firm delays actions as it invests less and accumulates cash. But, an imminent recession shortens its saving time, necessitating quick precautionary measures. Thus, as recession risk rises, the larger firm responds more by issuing preemptively and cutting investments and payouts. We estimate and validate our model.

Closing remarks