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A ruin model with dependence between claim sizes and claim intervals. (English) Zbl 1079.91048
Summary: We consider a generalization of the classical ruin model to a dependent setting, where the distribution of the time between two claim occurrences depends on the previous claim size. Exact analytical expressions for the Laplace transform of the ruin function are derived. The results are illustrated by several examples.

91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
[1] Adan, I., Kulkarni, V., 2003. Single-server queue with Markov dependent inter-arrival and service times. Queueing Systems 45 (2), 113-134. · Zbl 1036.90029
[2] Albrecher, H.; Kantor, J., Simulation of ruin probabilities for risk processes of Markovian type, Monte Carlo methods and applications, 8, 2, 111-127, (2002) · Zbl 1014.91055
[3] Asmussen, S., Matrix-analytic models and their analysis, Scandinavian journal of statistics, 27, 2, 193-226, (2000) · Zbl 0959.60085
[4] Asmussen, S., 2000b. Ruin Probabilities. World Scientific, Singapore. · Zbl 0960.60003
[5] Asmussen, S.; Schmidli, H.; Schmidt, V., Tail probabilities for non-standard risk and queueing processes with subexponential jumps, Advances in applied probability, 31, 2, 422-447, (1999) · Zbl 0942.60033
[6] Boxma, O.; Perry, D., A queueing model with dependence between service and interarrival times, European journal of operational research, 128, 3, 611-624, (2001) · Zbl 0996.90034
[7] Cohen, J.; Down, D., On the role of rouché’s theorem in queueing analysis, Queueing systems, 23, 281-291, (1996) · Zbl 0879.60097
[8] Combé, M., Boxma, O., 1998. BMAP modelling of a correlated queue. In: Walrand, J., Bagchi, K., Zobrist, G. (Eds.), Network Performance Modeling and Simulation. Gordon & Breach, Newark, pp. 177-196.
[9] Mikosch, T.; Samorodnitsky, G., Ruin probability with claims modeled by a stationary ergodic stable process, Annals of probability, 28, 4, 1814-1851, (2000) · Zbl 1044.60028
[10] Mikosch, T.; Samorodnitsky, G., The supremum of a negative drift random walk with dependent heavy-tailed steps, Annals of applied probability, 10, 3, 1025-1064, (2000) · Zbl 1083.60506
[11] Müller, A.; Pflug, G., Asymptotic ruin probabilities for risk processes with dependent increments, Insurance: mathematics and economics, 28, 3, 381-392, (2001) · Zbl 1055.91055
[12] Nyrhinen, H., Rough descriptions of ruin for a general class of surplus processes, Advances in applied probability, 30, 1008-1026, (1998) · Zbl 0932.60046
[13] Nyrhinen, H., Large deviations for the time of ruin, Journal of applied probability, 36, 3, 733-746, (1999) · Zbl 0947.60048
[14] Spiegel, M., 1965. Theory and Problems of Laplace Transforms. Schaum, New York.
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