Asymptotics of ruin probabilities for controlled risk processes in the small claims case

Scandinavian Actuarial Journal

Volumn 2004, Issue 5, 2004, Pages 321-335

  Hipp, Christian ^a   Schmidli, Hanspeter ^b  

^a University of Firenze ^*  (Germany)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Adjustment coefficient; Change of measure; Cramer Lundberg approximation; Geometric Browninan motion; Lundberg bounds; Martingale; Optimal control; Ruin probability

Indexed keywords

EID: 85014943199     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461230410000538     Document Type: Article

References (17)

1. Dufresne, F. & Gerber, H. U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Math. Econom. 10, 51-59.
2. Furrer, H. J. & Schmidli, H. (1994). Exponential inequalities for ruin probabilities of risk processes perturbed by diffusion. Insurance: Math. Econom. 15, 23-36.
3. Gaier, J., Grandits, P. & Schachermeyer, W. (2003). Asymptotic ruin probabilities and optimal investment. Ann. Appl. Probab. 13, 1054-1076.
4. Gerber, H. U. (1969). Entscheidungskriterien fur den zusammengesetzten Poisson-Prozess. Schweiz. Verein. Versicherungsmath. Mitt. 69, 185-228.
5. Grandits, P. (2003). An analogue of the Cramer-Lundberg approximation in the optimal investment case, Preprint, Technical University Vienna.
6. Hipp, C. & Plum, M. (2000). Optimal investment for insurers. Insurance: Math. Econom. 27, 215-228.
7. Hipp, C. & Plum, M. (2003). Optimal investment for investors with state dependent income, and for insurers. Finance and Stochastics 7, 299-321.
8. Hojgaard, B. (2000). Optimal dynamic premium control in non-life insurance. Maximizing dividend pay-outs. Preprint, University of Aalborg.
9. Hojgaard, B. & Taksar, M. (1998). Optimal proportional reinsurance policies for diffusion models. Scand. Actuarial J., 166-180.
10. Hojgaard, B. & Taksar, M. (1998). Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance Math. Econom. 22, 41-51.
11. Palmowski, Z. & Rolski, T. (2002). A technique for exponential change of measure for Markov processes. Bernoulli 8, 767-785.
12. Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. L. (1999). Stochastic Processes for Insurance and Finance. Chichester: Wiley.
13. Schmidli, H. (1995). Cramer-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion. Insurance: Math. Econom. 16, 135-149.
14. Schmidli, H. (2001). Optimal proportional reinsurance policies in a dynamic setting. Scand. Actuarial J. 55-68.
15. Schmidli, H. (2001). Risk processes conditioned on ruin. Working paper 176, Laboratory of Actuarial Mathematics, University of Copenhagen.
16. Schmidli, H. (2002). On minimising the ruin probability by investment and reinsurance. Ann. Appl. Probab. 12, 890-907.
17. Schmidli, H. (2002). Asymptotics of ruin probabilities for risk processes under optimal reinsurance policies. Manuscript, Laboratory of Actuarial Mathematics, University of Copenhagen.