Indicator Function and Hattendorff Theorem

Abstract

This paper presents an integration-by-parts proof of the Hattendorff theorem in the general fully continuous insurance model. The proof motivates a derivation of the theorem in the general fully discrete insurance model. Increments of a martingale over disjoint time intervals are uncorrelated random variables; the paper explains that the Hattendorff theorem can be viewed as an application of this result. A notable feature of the paper is the extensive use of the indicator function.