Abstract
The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.
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