Filip Zivanovic (Stony Brook University)
Modified necklace Lie bialgebras & quartic BV structures in supercategories abstract
Abstract:
In this talk, I will present the computation of algebraic multiplicities in Hilbert schemes of points on certain symplectic surfaces S. These spaces arise as Moduli spaces of Higgs bundles, and in the conjectural Kapustin-Witten mirror symmetry of these spaces, these multiplicities show up naturally, hence the motivation for this work.On the other hand, we also compute the Floer-theoretic filtration, previously connected to the multiplicities for these surfaces S themselves, realising that in their Hilbert schemes, these two invariants somewhat diverge from each other, discovering different geometric data of the space. Joint work with Alexandre Minets.
10:15 • Université de Genève, Conseil Général 7-9, Room 1-07
Patrick Wong (Monash University)
Valuation of variable annuities in a general stochastic environment abstract
Abstract:
This paper develops an advanced analytical framework for pricing Guaranteed Minimum Maturity Benefits (GMMB) within a stochastic environment featuring general dependencies. The model assumes stochastic dynamics for jump intensity, interest rates, and volatility, explicitly incorporating interdependencies among these risk factors. A significant contribution of this research is the derivation of analytical, closed-form solutions for pricing, as well as the computation of first, second, and mixed (cross) sensitivities to model parameters. These higher-order derivatives are obtained efficiently using the derivative of the matrix exponential. Despite the high flexibility of the model, our method ensures that both pricing and risk management remain computationally efficient.
11:00 • EPF Lausanne, Extranef 125