We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence 𝑋𝑡+1=𝐴𝑡𝑋𝑡+𝐵𝑡 , where 𝐴𝑡 and 𝐵𝑡 are non-negative random variables. We establish novel order-preserving properties, which enable us to obtain comparison theorems...

Multivariate random sums appear in many scientific fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case,...