Geodesic
The Cramer--Lundberg model with stochastic premium process
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 549-553

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In this paper the problem of ruin is considered for an insurance company. The premium process is a linear function of time in the classic Cramer–Lundberg model. The premium process is stochastic and it is also independent of a risk process. The nonruin probability is chosen as a measure of the payment ability. Integral equations and exponential bounds are obtained similarly with the classic Cramer–Lundberg model. That model with a discounting factor was also investigated in [L. S. Jilina, Prikladna Statistika, Aktuarna ta Finansova Matematika, 1 (2000), pp. 67–78 (in Russian)].
Keywords: Cramer–Lundberg model, stochastic premiums, integral equation, exponential bounds, adjustment coefficient.
Mots-clés : martingale 
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     author = {A. V. Boikov},
     title = {The {Cramer--Lundberg} model with stochastic premium process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a7/}
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A. V. Boikov. The Cramer--Lundberg model with stochastic premium process. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 549-553. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a7/