Speaker at 14:15: Zeshu Xu (BI Norwegian Business School)
Title: Demographics and Technology Adoption
Abstract: The share of young has declined in all major economies. I study the consequence of this trend in a dynamic model with (1) technological waves that arrive at random times, and (2) a labor market friction that the young are more adoptive to technological changes. Firms with differing technologies enter the economy as a result of directed research and development (R&D) investments driven by differing expected profits across old and new technologies. I show that a smaller share of the young population leads to a tighter labor market, and therefore lower R&D investments, slower adoption of new technologies, lower economic growth, and higher consumption volatility.
Speaker at 15:00: Ahmed Kebaier (Université d’Evry Paris-Saclay)
Title: Approximation of Stochastic Volterra Equations with kernels of completely monotone type
Abstract: In this work, we develop a multifactor approximation for d-dimensional Stochastic Volterra Equations (SVE) with Lipschitz coefficients and kernels of completely monotone type that may be singular. First, we prove an L²-estimation between two SVEs with different kernels, which provides a quantification of the error between the SVE and any multifactor Stochastic Differential Equation (SDE) approximation. For the particular rough kernel case with Hurst parameter lying in (0, 1/2), we propose various approximating multifactor kernels, state their rates of convergence and illustrate their efficiency for the rough Bergomi model. Second, we study a Euler discretization of the multifactor SDE and establish a convergence result towards the SVE that is uniform with respect to the approximating multifactor kernels. These obtained results lead us to build a new multifactor Euler scheme that reduces significantly the computational cost in an asymptotic way compared to the Euler scheme for SVEs. Finally, we show that our multifactor Euler scheme outperforms the Euler scheme for SVEs for option pricing in the rough Heston model.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to finance, economy, energy markets and production, but also to physics and biology. This series brings together the major research themes of the group. STAR stands for STochastics And Risk! Welcome!