Stochastic Modelling of An Expense-Augmented Insurance Portfolio Loss Process

Abstract

The present study aims to formulate, stochastically, the expense-augmented insurance portfolio loss process. To solve the problem, we consider a mixed compound stochastic process which constitutes expenses driven by a Gamma process and claims driven by an exponential distribution, and their intensity process is affine and known as the basic affine jump diffusion process (BAJDP) which is tractable and integrable and aids in capturing the randomness inherent in the insurance data. The statistical properties of the intensity process are explored and the numerical analysis shows a great reduction in the expected value of the loss process. Reducing the money outgo in the insurance business enhances retention, leading to financial stability if such is investigated.