10.30 - 11.15: Delia COCULESCU
11.15 - 12.00: Stefano PAGLIARANI
12.00 - 12.45: Guido GAZZANI
12.45 - 14.30: lunch break
14.30 - 15.30: colloquium by Yilin Wang
15.30 - 16.00: coffee break
16.00 - 16.45: Peter TANKOV
16.45 - 17.30: Sara BIAGINI
ABSTRACTS:
Delia COCULESCU (University of Zurich)
Title: Some principles of cooperative pricing in insurance
Abstract: We show how cooperative game theory can be effective for pricing insurance contracts in the presence of insolvency risk. Relying on the power of agents of forming coalitions and their desire of paying the least of costs for same payoffs, it is possible to identify "pricing measures", even in the case of some specific non-convex games. This feature of non-convexity appears as a consequence of the insolvency risk, impacting the players’ payoffs. We establish simple evaluation formulas, where in equilibrium, premia equal the expected value of the defaultable payoffs, under such absolutely continuous "pricing measures". Based on work with Ph. Arzner, F. Delbaen and K.-T. Eisele.
Stefano PAGLIARANI (University of Bologna)
Title: Degenerate McKean-Vlasov equations with singular dirft
Abstract: We study a class of McKean-Vlasov stochastic differential equations (MKV SDEs) with degenerate diffusion, a kinetic Langevin-type model being a particular instance. The MKV interaction acts on the drift through the multiplication between the density of the solution and a distribution that belongs to suitable anisotropic Besov space. These equations can be understood as mean-field limits of particle systems with singular moderate interactions. We prove well-posedness for the non-linear singular martingale problem associated to the MKV SDE and obtain partial regularity results for the density of the time-marginals. The approach combines analytical and probabilistic tools. As a by-product, we obtain well-posedness and stability results for the relevant non-linear singular Fokker-Planck and singular Kolmogorov backward PDEs, and the well-posedness of the linear kinetic-type singular martingale problem. This is a joint work with Elena Issoglio, Francesco Russo and Davide Trevisani.
Guido GAZZANI (University of Verona)
Title: Polynomial path-dependent volatility models
Abstract: Path-dependent volatility models have been receiving growing attention from both researchers and practitioners in recent years. Most of these models reproduce a wide range of stylized facts that are well known to underlie the volatility process. We build on the work of Guyon and Lekeufack (2023), where after an empirical study comparing different models a simple parametrization of the volatility process was introduced. The main features consist in exponentially weighted past returns and past returns squared. Although simple, the former model homogeneous in volatility, comes with several computational challenges that can only be overcome using machine-learning techniques (see Gazzani and Guyon (2024)). Here, we take a step back in favor of mathematical tractability, dealing with a similar model that is homogeneous in variance. We call this class polynomial path-dependent volatility (PDV) models. We tackle existence, uniqueness, and absence of explosion of the SDE and we derive conditions for the non-negativity/positivity of the variance process. Calibration to real market data benefits from the fast computation of the VIX via the moment formula, and an empirical study demonstrates strong performance under the physical measure. Finally, we compute the model's forward variance, a result that lays the foundation for studying its dynamical properties. This talk is based on joint work with Fabio Baschetti and Julien Guyon.
Sara BIAGINI (LUISS University)
Title: Climate risk mitigation via carbon markets: accounting for the lifespan of GHGs
Abstract: We study the problem of optimal climate risk mitigation with short-term emission reduction targets and long-run temperature stabilization goals in the presence of firms generating greenhouse gases with different temporal persistency and warming potential. We investigate how the pervasive notion of carbon equivalence may undermine climate risk mitigation efforts when carbon markets can be used to trade short-lived gasses against long-lived ones. The findings demonstrate the vulnerability of certain emission metrics and carbon accounting standards to greenwashing and support the reporting of emissions in disaggregated form and native units of measure. Based on a joint work with E. Biffis and K. Salehzadeh Nobari.
Peter TANKOV (ENSAE Paris)
Title: A model of strategic sustainable investment
Abstract: We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics and may spend part of its revenues towards emission reduction (e.g., renovating the infrastructure). The firm's objective is to maximize the discounted expectation of a function of its profits. The investor participates in the profits, may decide to invest to support the firm's production capacity and uses a profit function which accounts for both financial and environmental factors. Nash equilibria of the game are obtained via a system of variational inequalities. We formulate a general verification theorem for this system in a diffusive setup and construct an explicit solution in the zero-noise limit. Our explicit results and numerical approximations show that both the investor's and the firm's optimal actions are triggered by moving boundaries that increase with the total amount of emission abatement. Joint work with Tiziano De Angelis and Caio César Graziani Rodrigues.