Monotone Stochastic Order of Processes with Independent Increments
In this article we study monotone stochastic orders for real-valued processes with independent increments and derive sufficient deterministic conditions which are easy to verify and suitable for applications. Our proof is based on an explicit construction of a coupling. We also derive comparison results for L\'evy processes and semimartingales with conditionally independent increments.
We are considering sequences P1, P2,... of (mechanistic) price indices, where Pn+1 is a price index which depends on the 4n (base time and comparison time) quantities and prices of the price index Pn and, in addition, on the 4 (base time and comparison time) quantities and prices of a (n+1)th commodity. Without any differentiability or continuity assumption it is being shown that a system of three very weak axioms on the P’s together with a rather generally looking extension rule that connects Pn+1 with Pn yields sequences whose terms depend only on the price ratios pi/p i O , where p i O is the base price and pi is the current price of commodity i.