UCSB Financial Math
Student Seminar (FMSS)

Abstract:
Variance-mean mixtures of Gaussian distributions provide a flexible framework for modeling skewed and heavy-tailed multivariate data. In this talk, we introduce multiple-scaled extensions based on both coordinatewise mixing and mixing along principal directions of the covariance structure. These approaches allow latent scaling variables to act separately across dimensions or eigendirections, providing enhanced flexibility for modeling heterogeneous skewness and tail behavior while preserving a coherent multivariate dependence structure. Particular attention is given to the Multiple-Scaled Generalized Asymmetric Laplace model, obtained through gamma-based mixing. We discuss key distributional properties and parameter estimation via the EM algorithm, with applications to modeling the joint distribution of asset returns.

Abstract:
We study a continuous-time, non-zero-sum stochastic game model to analyze the competitive transition of economic sectors toward green technology. We model two economic agents who determine their optimal timing for an irreversible switch to zero-emission production while simultaneously managing continuous capital investment strategies. Strategic interactions are explicitly captured through a global temperature state, θ, which evolves as a function of cumulative emissions, thereby inducing climate-related damage that erodes the profitability of non-green production. The resulting game is structured as a system of regime-dependent stopping games, indexed by the decarbonization status of the players and their respective production capacities, X_i (i = 1, 2). We characterize the Markov Nash equilibrium via a system of coupled Hamilton-Jacobi-Bellman (HJB) equations, which exhibit varying dimensionality as the game transitions between different technology regimes. Our numerical analysis reveals that strategic interplay can either accelerate or delay the transition relative to a single-player benchmark, contingent upon prevailing production levels and climate damage intensity. Furthermore, we demonstrate that policy interventions, such as carbon taxation, shift the endogenous switching frontiers in predictable ways, providing a mechanism to mitigate strategic delay and facilitate a more efficient transition.