Path-Space and Random Dynamical Systems Formulation of the Cramér-Lundberg Surplus Process

Uçar E.

7th European Actuarial Journal Conference , İstanbul, Türkiye, 9 - 11 Eylül 2026, ss.23, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.23
  • Ankara Üniversitesi Adresli: Evet

Özet

This paper develops a path-space and random dynamical systems formulation of the classical Cramér–Lundberg surplus process on a finite time horizon. We represent surplus sample paths as elements of a Skorokhod space of Cádlág functions and introduce a natural time-shift operator acting on trajectories. We then model the claim stream as a shifted random environment and express the surplus evolution as a measurable cocycle over the corresponding base shift. This yields a cocycle-based pathwise representation of the surplus process. The contribution is theoretical and structural. It provides a mathematically explicit framework for the study of surplus evolution as a dynamical object on a finite horizon.