Ruin probabilities and penalty functions with stochastic rates of interest

Stochastic Processes and their Applications

Volumn 112, Issue 1, 2004, Pages 53-78

  Cai, Jun ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Brownian motion; Compound Poisson process; Integral equation; Integro differential equation; L vy process; Penalty function; Ruin theory; Stochastic rates of interest; Subordinator

Indexed keywords

EID: 2542499687     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2004.01.007     Document Type: Article

References (19)

1. Asmussen S. Ruin Probabilities 2000 World Scientific Singapore
2. Cai J. Ruin probabilities under dependent rates of interest J. Appl. Probab. 39 2002 312-323
3. Cai J. Dickson D.C.M. On the expected discounted penalty function at ruin of a surplus process with interest Insurance Math. Econom. 30 2002 389-404
4. Cai J. Dickson D.C.M. Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest Insurance Math. Econom. 32 2003 61-71
5. Carmona P. Petit F. Yor M. On exponential functionals of certain Lévy processes Stochastics Stochastic Rep. 47 1994 71-101
6. Dufresne F. Gerber H.U. Risk theory for the compound Poisson process that is perturbed by diffusion Insurance Math. Econom. 10 1991 51-59
7. Frolova A. Kabanov Y. Pergamenshchikov S. In the insurance business risky investments are dangerous Finance Stoch 6 2002 227-235
8. Gerber H.U. Shiu E.S.W. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin Insurance Math. Econom. 21 1997 129-137
9. Grandell J. Aspects of Risk Theory 1991 Springer New York
10. Kalashnikov V. Norberg R. Power tailed ruin probabilities in the presence of risky investments Stochastic Process. Appl. 98 2002 211-228
11. Norberg R. Ruin probabilities with assets and liabilities of diffusion type Stochastic Process. Appl. 81 1999 255-269
12. Paulsen J. Risk theory in a stochastic environment Stochastic Process. Appl. 21 1993 327-361
13. Paulsen J. On Cramér-like asymptotics for risk processes with stochastic return on investments Ann. Appl. Probab. 12 2002 1247-1260
14. Paulsen J. Gjessing H.K. Ruin theory with stochastic economic environment Adv. Appl. Probab. 29 1997 965-985
15. Rolski T. Schmidli V. Schmidt V. Teugels J.L. Stochastic Processes for Insurance and Finance 1999 Wiley Chichester
16. Sundt B. Teugels J.L. Ruin estimates under interest force Insurance Math. Econom. 16 1995 7-22
17. Wang G. Wu R. Distributions for the risk process with a stochastic return on investments Stochastic Process. Appl. 95 2001 329-341
18. Willmot G.E. Lin X.S. Lundberg Approximations for Compound Distributions with Insurance Applications 2001 Springer New York
19. Yor M. On some exponential functionals of Brownian motion Adv. Appl. Probab. 24 1992 509-531