A0802
Title: Limit theorems for dynamical compound Poisson processes
Authors: Juho Leppanen - Tokai University (Japan) [presenting]
Yushi Nakano - Hokkaido University (Japan)
Jun Hirano - Tokai University (Japan)
Abstract: The classical compound Poisson process, widely used in actuarial mathematics and other fields, assumes that claim amounts (or jump sizes) are independent and identically distributed (i.i.d.). This assumption is too restrictive in many real-world applications. The i.i.d. condition is relaxed by modeling claim amounts as observations along the trajectory of a hyperbolic dynamical system, such as a smooth expanding map on a compact Riemannian manifold. Limit theorems are presented for these dynamical compound Poisson processes, including a large deviation principle and a central limit theorem with Wasserstein-2 and Kolmogorov error bounds.
