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Modern Stochastics: Theory and Applications


A change of measures technique for compound mixed renewal processes with applications in Risk Theory
Pub. online: 12 August 2025      Type: Research Article      Open accessOpen Access
Received
4 April 2025
Accepted
30 June 2025
Published
12 August 2025

Abstract

Given a compound mixed renewal process S under a probability measure P, we provide a characterization of all progressively equivalent martingale probability measures Q on the domain of P, that convert S into a compound mixed Poisson process. This result extends earlier works of Delbaen and Haezendonck, Lyberopoulos and Macheras, and the authors, and enables us to find a wide class of price processes satisfying the condition of no free lunch with vanishing risk. Implications to the ruin problem and to the computation of premium calculation principles in an arbitrage-free insurance market are also discussed.

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© 2025 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Compound mixed renewal processes change of measures martingales premium calculation principles ruin probability

MSC2020
91G05 60G55 28A35 60A10 60G44 60K05

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