`a`
Journal of Industrial and Management Optimization (JIMO)
 

A note on a Lévy insurance risk model under periodic dividend decisions
Page number are going to be assigned later 2017

doi:10.3934/jimo.2017036      Abstract        References        Full text (437.7K)      

Zhimin Zhang - College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China (email)
Eric C. K. Cheung - Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China (email)

1 H. Albrecher, E. C. K. Cheung and S. Thonhauser, Randomized observation periods for the compound Poisson risk model: Dividends, ASTIN Bulletin, 41 (2011), 645-672.       
2 H. Albrecher, E. C. K. Cheung and S. Thonhauser, Randomized observation periods for the compound Poisson risk model: The discounted penalty function, Scandinavian Actuarial Journal, 2013 (2013), 424-452.       
3 H. Albrecher and H. U. Gerber, A note on moments of dividends, Acta Mathematicae Applicatae Sinica, English Series, 27 (2011), 353-354.       
4 H. Albrecher, J. Ivanovs and X. Zhou, Exit identities for Lévy processes observed at Poisson arrival times, Bernoulli, 22 (2016), 1364-1382.       
5 H. Albrecher, J.-F. Renaud and X. Zhou, A Lévy insurance risk process with tax, Journal of Applied Probability, 45 (2008), 363-375.       
6 S. Asmussen, Applied Probability and Queues, $2^{nd}$ edition, Springer-Verlag, New York, 2003.       
7 S. Asmussen and H. Albrecher, Ruin Probabilities, $2^{nd}$ edition, World Scientific, New Jersey, 2010.       
8 S. Asmussen, F. Avram and M. Usabel, Erlangian approximations for finite-horizon ruin probabilities, ASTIN Bulletin, 32 (2002), 267-281.       
9 B. Avanzi, E. C. K. Cheung, B. Wong and J.-K. Woo, On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency, Insurance: Mathematics and Economics, 52 (2013), 98-113.       
10 E. Biffis and M. Morales, On a generalization of the Gerber-Shiu function to path-dependent penalties, Insurance: Mathematics and Economics, 46 (2010), 92-97.       
11 P. Carr, Randomization and the American put, Review of Financial Studies, 11 (1998), 597-626.
12 E. C. K. Cheung, A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium, Insurance: Mathematics and Economics, 48 (2011), 384-397.       
13 E. C. K. Cheung, D. C. M. Dickson and S. Drekic, Moments of discounted dividends for a threshold strategy in the compound Poisson risk model, North American Actuarial Journal, 12 (2008), 299-318.
14 I. Czarna and Z. Palmowski, Ruin probability with Parisian delay for a spectrally negative Lévy risk process, Journal of Applied Probability, 48 (2011), 984-1002.       
15 D. C. M. Dickson and C. Hipp, On the time to ruin for Erlang(2) risk processes, Insurance: Mathematics and Economics, 29 (2001), 333-344.       
16 D. C. M. Dickson and H. R. Waters, Some optimal dividends problems, ASTIN Bulletin, 34 (2004), 49-74.       
17 F. Dufresne and H.U. Gerber, Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance: Mathematics and Economics, 10 (1991), 51-59.       
18 R. Feng, A matrix operator approach to the analysis of ruin-related quantities in the phase-type renewal risk model, Bulletin of the Swiss Association of Actuaries, 2009 (2009), 71-87.       
19 R. Feng and Y. Shimizu, On a generalization from ruin to default in a Lévy insurance risk model, Methodology and Computing in Applied Probability, 15 (2013), 773-802.       
20 H. Furrer, Risk processes perturbed by $\alpha$-stable Lévy motion, Scandinavian Actuarial Journal, 1998 (1998), 59-74.       
21 J. Garrido and M. Morales, On the expected discounted penalty function for Lévy risk processes, North American Actuarial Journal, 10 (2006), 196-218.       
22 H. U. Gerber, An Introduction to Mathematical Risk Theory, Huebner Foundation Monograph 8, Richard D. Irwin: Homewood, Illinois, 1979.       
23 H. U. Gerber and E. S. W. Shiu, On optimal dividends: From reflection to refraction, Journal of Computational and Applied Mathematics, 186 (2006), 4-22.       
24 H. U. Gerber and E. S. W. Shiu, On the time value of ruin, North American Actuarial Journal, 2 (1998), 48-78.       
25 H. U. Gerber and E. S. W. Shiu, Optimal dividends: Analysis with Brownian Motion, North American Actuarial Journal, 8 (2004), 1-20.       
26 M. Huzak, M. Perman, H. Šikić and Z. Vondraček, Ruin probabilities and decompositions for general perturbed risk processes, Annals of Applied Probability, 14 (2004), 1378-1397.       
27 A. E. Kyprianou, Fluctuations of Lévy Processes with Applications: Introductory Lectures, $2^{nd}$ edition, Springer-Verlag, Berlin Heidelberg, 2014.       
28 A. E. Kyprianou, Gerber-Shiu Risk Theory, Springer, Cham Heidelberg New York Dordrecht London, 2013.       
29 A. E. Kyprianou and R. L. Loeffen, Refracted Lévy processes, Annales de l'Institut Henri Poincaré - Probabilités et Statistiques, 46 (2010), 24-44.       
30 A. E. Kyprianou and Z. Palmowski, Distributional study of De Finetti's dividend problem for a general Lévy insurance risk process, Journal of Applied Probability 44 (2007), 428-443.       
31 A. E. Kyprianou and Z. Palmowski, Fluctuations of spectrally negative Markov additive process, Séminaire de Probabilitiés XLI, Lecture Notes in Mathematics, 1934 (2008), 121-135.       
32 A. E. Kyprianou and M. R. Pistorius, Perpetual options and Canadization through fluctuation theory, Annals of Applied Probability, 13 (2003), 1077-1098.       
33 A. E. Kyprianou and X. Zhou, General tax structures and the Lévy insurance risk model, Journal of Applied Probability, 46 (2009), 1146-1156.       
34 X. S. Lin, G. E. Willmot and S. Drekic, The compound Poisson risk model with a constant dividend barrier: Analysis of the Gerber-Shiu discounted penalty function, Insurance: Mathematics and Economics, 33 (2003), 551-566.       
35 B. G. Lindsay, R. S. Pilla and P. Basak, Moment-based approximations of distributions using mixtures: Theory and applications, Annals of the Institute of Statistical Mathematics, 52 (2000), 215-230.       
36 R. Loeffen, I. Czarna and Z. Palmowski, Parisian ruin probability for spectrally negative Lévy processes, Bernoulli, 19 (2013), 599-609.       
37 J.-F. Renaud and X. Zhou, Distribution of the present value of dividend payments in a Lévy risk model, Journal of Applied Probability, 44 (2007), 420-427.       
38 V. Ramaswami, D. G. Woolford and D. A. Stanford, The Erlangization method for Markovian fluid flows, Annals of Operations Research, 160 (2008), 215-225.       
39 Z. B. Salah and M. Morales, Lévy systems and the time value of ruin for Markov additive processes, European Actuarial Journal, 2 (2012), 289-317.       
40 H. Schmidli, Distribution of the first ladder height of a stationary risk process perturbed by $\alpha$-stable Lévy motion, Insurance: Mathematics and Economics, 28 (2001), 13-20.       
41 D. A. Stanford, F. Avram, A. L. Badescu, L. Breuer, A. Da Silva Soares and G. Latouche, Phase-type approximations to finite-time ruin probabilities in the Sparre-Anderson and stationary renewal risk models, ASTIN Bulletin, 35 (2005), 131-144.       
42 D. A. Stanford, K. Yu and J. Ren, Erlangian approximation to finite time ruin probabilities in perturbed risk models, Scandinavian Actuarial Journal, 2011 (2011), 38-58.       
43 C. C.-L. Tsai and G. E. Willmot, A generalized defective renewal equation for the surplus process perturbed by diffusion, Insurance: Mathematics and Economics, 30 (2002), 51-66.       
44 Z. Zhang, On a risk model with randomized dividend-decision times, Journal of Industrial and Management Optimization, 10 (2014), 1041-1058.       
45 Z. Zhang and E. C. K. Cheung, The Markov additive risk process under an Erlangized dividend barrier strategy, Methodology and Computing in Applied Probability, 18 (2016), 275-306.       
46 Z. Zhang, E. C. K. Cheung and H. Yang, Lévy insurance risk process with Poissonian taxation, Scandinavian Actuarial Journal, 2017 (2017), 51-87.       
47 Z. Zhang, C. Liu and Y. Yang, On a perturbed compound Poisson model with varying premium rates, Journal of Industrial and Management Optimization, 13 (2017), 721-736.       

Go to top