The Center for Mathematical Economics organizes regularly seminars on Mathematical Finance / Financial Economics within the Bielefeld Stochastic Afternoon. This term's program is below.
First Speaker: Giovanna Apicella (University of Udine)
Title: Longevity risk modeling: bridging actuarial and behavioral perspectives
Abstract:
The paper investigates why individuals' subjective survival expectations systematically differ from objective actuarial survival probabilities. In particular, consistent empirical evidence shows that individuals aged approximately 50–70 years tend to underestimate their survival prospects, while older individuals tend to overestimate them.
To explain this pattern, we develop a theoretical model in which survival beliefs’ updating is affected by psychological sentiment rather than solely by objective health information. Individuals alternate between optimistic and pessimistic states, which affect how they interpret and react to observed health shocks and update their survival beliefs. The model shows that persistent optimism, or a greater tendency to shift from pessimism to optimism, can generate the observed age-dependent pattern of subjective survival beliefs.
Using longitudinal data from the Survey of Health, Ageing and Retirement in Europe (SHARE), we empirically analyse the predictions of the model and find a consistent sentiment-driven update of probabilities.
The findings highlight the relevance of behavioral biases in longevity risk assessment, with implications for retirement planning, savings decisions, and insurance demand.
Second Speaker: Salvatore Federico (University of Bologna)
Title: Mean Field Games in Hilbert Spaces
Abstract:
We study Mean Field Games (MFG) systems in real separable infinite-dimensional Hilbert spaces, addressing both general nonlinear formulations and the specific linear-quadratic (LQ) case. In the general setting, the MFG system consists of a second-order parabolic Hamilton-JacobiBellman(HJB)equation coupled with a nonlinear Fokker-Planck (FP) equation, both involving Kolmogorov operators. Solutions are interpreted respectively in the mild and weak senses, and we establish well-posedness via Tikhonov’s fixed point theorem, with uniqueness ensured under separability and Lasry-Lions-type monotonicity conditions. In the LQ framework, we focus on the case where the mean field interaction enters only through the objective functional via the mean of the distribution. This structure allows the reduction of the MFG system to a Riccati equation and a forward-backward system of abstract evolution equations—an approach that is novel in infinite dimensions. Existence and uniqueness are obtained through a refined approximation method, and the theory is applied to a production output planning problem with delayed control.
Third Speaker: Maria-Laura Torrente (Università degli Studi di Genova)
Title: An Algebraic Perspective on Game-Theoretic Equilibria
Abstract:
Polynomial formulations provide a common framework for studying the existence, computation, and structure of game-theoretic equilibria.
Starting from Nash equilibria, we discuss algebraic approaches to Berge equilibria and ongoing work on A-equilibria, including some existence results.
Stability issues under payoff perturbations are also discussed as a direction for further investigation.
First Speaker: Marco Frittelli (Università degli Studi di Milano)
Title: Collective Arbitrage, Pareto Improvements and Pareto Optimality
Abstract: This paper advances the theory of Collective Finance, as developed in Biagini, F., et al. "Collective arbitrage and the value of cooperation." (2026), Doldi, A. et al. "Collective completeness and pricing hedging duality." (2025), Doldi, A. et al. "When cooperation is beneficial to all agents." (2026) and Frittelli, M. "Collective free lunch and the FTAP." (2025). Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents’ preferences and collective pricing measures. The framework applies to both continuous and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent’s indirect utility.
Second Speaker: Marco Maggis (Università degli Studi di Milano)
Title: Collective Arbitrage, Pricing and Market Completeness
Abstract: In this talk, we explore how cooperation among financial agents reshapes the classical notions of arbitrage, pricing, and market completeness. We consider a multi-agent framework in which agents trade in potentially different submarkets and cooperate through suitable risk-sharing mechanisms. We first introduce the notion of collective arbitrage and show how cooperation may generate arbitrage opportunities that are not accessible to individual agents, while also reducing super-replication costs. We then present a collective version of the First Fundamental Theorem of Asset Pricing, together with a pricing-hedging duality, characterizing the absence of collective arbitrage through suitable families of equivalent martingale measures. Finally, we introduce collective replication and completeness and establish a collective Second Fundamental Theorem of Asset Pricing. In particular, we discuss how cooperation can lead to collective market completeness even when the individual markets are incomplete.
First Speaker: Paolo Guasoni (Dublin City University)
Title: tba
Abstract:
Second Speaker: Alpar Meszaros (Durham University)
Title: tba
Abstract: