Large deviations for risk processes with reinsurance

Journal of Applied Probability

Volumn 43, Issue 3, 2006, Pages 713-728

  Macci, Claudio ^a   Stabile, Gabriele ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Large deviations; Lundberg estimate; Reinsurance; Risk process; Ruin probability

Indexed keywords

EID: 34047109124     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1158784941     Document Type: Article

References (14)

1. BALDI, P. AND PICCIONI, M. (1999). A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain. Statist. Prob. Lett. 41, 107-115.
2. BOROVKOV, A. A. (1967). Boundary value problems for random walks and large deviations in function spaces. Theory Prob. Appl. 12, 575-595.
3. DE ACOSTA, A. (1994). Large deviations for vector-valued Lévy processes. Stoch. Process. Appl. 51, 75-115.
4. DEMBO, A. AND ZEITOUNI, O. (1993). Large Deviations Techniques and Applications. Jones and Bartlett, Boston, MA.
5. DUFFIELD, N. G. AND O'CONNELL, N. (1995). Large deviations and overflow probabilities for a single server queue, with applications. Math. Proc. Camb. Phil. Soc. 118, 363-374.
6. HALD, M. AND SCHMIDLI, H. (2004). On the maximisation of the adjustment coefficient under proportional reinsurance. ASTIN Bull. 34, 75-83.
7. HIPP, C. AND VOGT, M. (2003). Optimal dynamic XL reinsurance. ASTIN Bull. 33, 193-207.
8. MACCI, C, AND TORRISI, G. L. (2004). Asymptotic results for perturbed risk processes with delayed claims. Insurance Math. Econom. 34, 307-320.
9. MACCI, C., STABILE, G. AND TORRISI, G. L. (2005). Lundberg parameters for non standard risk processes. Scand. Actuarial J. 2005, 417-432.
10. ROLSKI, T., SCHMIDLI, H., SCHMIDT, V. AND TEUGELS, J. L. (1999). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.
11. SCHMIDLI, H. (2001). Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuarial J. 2001, 55-68.
12. SCHMIDLI, H, (2002). Asymptotics of ruin probabilities for risk processes under optimal reinsurance policies: the small claim case. Working Paper 180, Laboratory of Actuarial Mathematics, University of Copenhagen.
13. SCHMIDLI, H. (2004). Asymptotics of ruin probabilities for risk processes under optimal reinsurance and investment policies: the large claim case. Queueing Systems 46, 149-157.
14. WATERS, H. R. (1983). Some mathematical aspects of reinsurance. Insurance Math. Econom. 2, 17-26.