A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process

Spyridon M. Tzaninis and Nikolaos D. Macheras

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Abstract: Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound mixed renewal process under Q with improved properties. As a consequence, we prove that any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures. Applications related to the ruin problem and to the computation of premium calculation principles in an insurance market without arbitrage opportunities are discussed in [26] and [27], respectively.

Date: 2020-07, Revised 2020-07
New Economics Papers: this item is included in nep-ias
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