Let ξ t be a classic risk process or a risk process with stochastic premiums. We establish conditions for balance between ruin and survival in the case of zero initial capital u = 0 (ruin probability q + = ψ(0) = 1/2, survival probability p + = 1 - q + = 1/2) and determine premium estimates under these conditions.
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References
H. Bühlmann, Mathematical Methods in Risk Theory, Springer, Berlin (1970).
D. V. Gusak, Processes with Independent Increments in Risk Theory [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2011).
D. V. Gusak, A. G. Kukush, A. M. Kulik, Yu. Mishura, and A. Yu. Pilipenko, Theory of Stochastic Processes with Applications to Financial Mathematics and Risk Theory, Springer, New York (2010).
D. V. Gusak, Limit Problems for Processes with Independent Increments in Risk Theory [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2007).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 7, pp. 988–993, July, 2012.
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Gusak, D.V. Conditions for balance between survival and ruin. Ukr Math J 64, 1128–1135 (2012). https://doi.org/10.1007/s11253-012-0703-4
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DOI: https://doi.org/10.1007/s11253-012-0703-4