There are extensive studies on the allocation problems in the field of insurance and finance. We observe that these studies, although involving different methodologies, share some inherent commonalities. In this paper, we develop a new framework for these studies with the tool of arrangement...

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...

Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, limiting their applicability. This paper...