A generalized defective renewal equation for the surplus process perturbed by diffusion

Citations

Cited by:

1. Franck Adékambi & Essodina Takouda, 2020. "Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence," Risks, MDPI, vol. 8(1), pages 1-25, March.
2. Runhuan Feng & Yasutaka Shimizu, 2013. "On a Generalization from Ruin to Default in a Lévy Insurance Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 773-802, December.
3. Christian Paroissin & Landy Rabehasaina, 2015. "First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 351-372, June.
4. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
5. Chi, Yichun & Lin, X. Sheldon, 2011. "On the threshold dividend strategy for a generalized jump-diffusion risk model," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 326-337, May.
6. Biffis, Enrico & Morales, Manuel, 2010. "On a generalization of the Gerber-Shiu function to path-dependent penalties," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 92-97, February.
7. Zhimin Zhang & Eric C. K. Cheung, 2016. "The Markov Additive Risk Process Under an Erlangized Dividend Barrier Strategy," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 275-306, June.
8. Ren, Jiandong, 2005. "The expected value of the time of ruin and the moments of the discounted deficit at ruin in the perturbed classical risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 505-521, December.
9. Franck Adékambi & Essodina Takouda, 2022. "On the Discounted Penalty Function in a Perturbed Erlang Renewal Risk Model With Dependence," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 481-513, June.
10. Tsai, Cary Chi-Liang, 2003. "On the expectations of the present values of the time of ruin perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 413-429, July.
11. Lu, Zhaoyang & Xu, Wei & Zhang, Yan & Sun, Yingling, 2009. "On the ruin probability for the Cox correlated risk model perturbed by diffusion," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 381-389, February.
12. Morales, Manuel, 2007. "On the expected discounted penalty function for a perturbed risk process driven by a subordinator," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 293-301, March.
13. Li, Shuanming & Lu, Yi, 2005. "On the expected discounted penalty functions for two classes of risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 179-193, April.
14. Li, Shuanming & Ren, Jiandong, 2013. "The maximum severity of ruin in a perturbed risk process with Markovian arrivals," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 993-998.
15. Tsai, Cary Chi-Liang & Sun, Li-juan, 2004. "On the discounted distribution functions for the Erlang(2) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 5-19, August.
16. Kolkovska, Ekaterina T. & Martín-González, Ehyter M., 2016. "Gerber–Shiu functionals for classical risk processes perturbed by an α-stable motion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 22-28.
17. Sarkar, Joykrishna & Sen, Arusharka, 2005. "Weak convergence approach to compound Poisson risk processes perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 421-432, June.
18. Yang, Hu & Zhang, Zhimin, 2009. "The perturbed compound Poisson risk model with multi-layer dividend strategy," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 70-78, January.
19. Chiu, S. N. & Yin, C. C., 2003. "The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 59-66, August.
20. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.
21. Mitric, Ilie-Radu & Sendova, Kristina P. & Tsai, Cary Chi-Liang, 2010. "On a multi-threshold compound Poisson process perturbed by diffusion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 366-375, March.
22. Kam C. Yuen & Yuhua Lu & Rong Wu, 2009. "The compound Poisson process perturbed by a diffusion with a threshold dividend strategy," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 73-93, January.
23. Riccardo Gatto & Benjamin Baumgartner, 2016. "Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 217-235, March.
24. Schmidli, Hanspeter, 2010. "On the Gerber-Shiu function and change of measure," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 3-11, February.
25. Tsai, Cary Chi-Liang, 2006. "On the stop-loss transform and order for the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 151-170, August.
26. Chi, Yichun & Jaimungal, Sebastian & Lin, X. Sheldon, 2010. "An insurance risk model with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 52-66, February.
27. Shimizu, Yasutaka & Zhang, Zhimin, 2017. "Estimating Gerber–Shiu functions from discretely observed Lévy driven surplus," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 84-98.
28. Tsai, Cary Chi-Liang & Willmot, Gordon E., 2002. "On the moments of the surplus process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 327-350, December.