Faculty of Economics and Business Administration Publications Database

Optimal prediction of compound mixed Poisson processes

Volume: 137
Number: 4
Pages: 1332 - 1342
Month: April
ISSN-Print: 0378-3758
Link External Source: Online Version
Year: 2007
Keywords: Compound Poisson process; Pólya–Lundberg process; Mixed Poisson process; Nonhomogeneous Poisson process; Best linear unbiased forecast; Risk theory

The paper examines best linear unbiased prediction of compound mixed Poisson processes where typical stipulations such as conditional or unconditional independence of the increments are weakened.

Explicit representations of the optimal forecast, its asymptotic distribution and the minimum mean square error are established. The article also discusses applications to special processes of risk theory including Pólya–Lundberg processes and nonstationary Poisson processes with time-dependent arrival rates.