Risk processes with shot noise Cox claim number process and reserve dependent premium rate |
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| Authors: | Claudio Macci Giovanni Luca Torrisi |
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| Institution: | a Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Rome, Italyb Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche (CNR), Via dei Taurini 19, I-00185 Rome, Italy |
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| Abstract: | We consider a suitable scaling, called the slow Markov walk limit, for a risk process with shot noise Cox claim number process and reserve dependent premium rate. We provide large deviation estimates for the ruin probability. Furthermore, we find an asymptotically efficient law for the simulation of the ruin probability using importance sampling. Finally, we present asymptotic bounds for ruin probabilities in the Bayesian setting. |
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| Keywords: | 60F10 91B30 |
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