折射Lévy风险过程的Parisian破产问题
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摘要
该文主要讨论了折射Lévy风险过程(Refracted Lévy risk processes)的Parisian破产问题.折射Lévy风险过程可以看作一个保费可作调整的风险过程.该文借助Lévy过程的尺度函数(scale function)以及波动性理论(fluctuation)给出了折射Lévy风险过程的Parisian破产概率的确切表达式.
In this paper, we investigate the Parisian ruin probability for a refracted Lévy process with b≥ 0 and derive the explicit formulas for Parisian ruin probability. Our methodology use fluctuation theory and the theory of scale functions for spectrally negative Levy processes.Two examples are provided.
In this paper, we investigate the Parisian ruin probability for a refracted Lévy process with b≥ 0 and derive the explicit formulas for Parisian ruin probability. Our methodology use fluctuation theory and the theory of scale functions for spectrally negative Levy processes.Two examples are provided.
引文
[1] Dassios A, Wu S. Parisian ruin with exponential claims. 2008, http://eprints.lse.ac.uk/32033/
[2] Czarna I, Palmowski Z. Ruin probability with Parisian delay for a spectrally negative Levy risk process.Journal of Applied Probability, 2011, 48(4):984-1002
[3] Loeffen R L, Czarna I, Palmowski Z. Parisian ruin probability for spectrally negative Levy processes.Bernoulli, 2013, 19(2):599-609
[4] Wong J T Y, Cheung E C K. On the time value of Parisian ruin in(dual)renewal risk processes with exponential jumps. Insurance Mathematics and Economics, 2015, 65(2):280-290
[5] Baurdoux E J, Pardo J C, Pérez J L. Gerber-Shiu distribution at Parisian ruin for Lévy insurance risk process. Journal of Applied Probability, 2015, 53(2):572-584
[6] Landrianlt D, Renaud J F, Zhou X. Occupation times of spectrally negative L6vy processes with applications. Stochastic Processes and Their Applications, 2011, 121(11):2629-2641
[7] Landrianlt D, Renaud J F, Zhou X. An insurance risk model with Parisian implementation delays. Methodology and Computing in Applied Probability, 2014, 16(3):583-607
[8] Lkabous M A, Czarna I, Renaud J F. Parisian ruin for a refracted Levy process. Insurance Mathematics and Economics, 2017, 74:153-163
[9] Kyprianou A E, Loeffen R L. Refracted Lévy processes. Ann Inst H PoincaréProbab Statist, 2010, 46(1):24-44
[10] Renaud J F. On the time spent in the red by a refracted Lévy risk process. Journal of Applied Probability,2013, 51(4):1171-1181
[11] Kyprianou A E. Introductory Lectures on Fluctuations of Levy Processes with Applications. Berlin:Springer, 2006, 42(4):37-57
[12] Loeffen R L, Renaud J F, Zhou X. Occupation times of intervals untill first passage times for spectrally negative Levy processes with applications. Stochastic Processes and Their Applications, 2014, 124(3):1408-1435
[2] Czarna I, Palmowski Z. Ruin probability with Parisian delay for a spectrally negative Levy risk process.Journal of Applied Probability, 2011, 48(4):984-1002
[3] Loeffen R L, Czarna I, Palmowski Z. Parisian ruin probability for spectrally negative Levy processes.Bernoulli, 2013, 19(2):599-609
[4] Wong J T Y, Cheung E C K. On the time value of Parisian ruin in(dual)renewal risk processes with exponential jumps. Insurance Mathematics and Economics, 2015, 65(2):280-290
[5] Baurdoux E J, Pardo J C, Pérez J L. Gerber-Shiu distribution at Parisian ruin for Lévy insurance risk process. Journal of Applied Probability, 2015, 53(2):572-584
[6] Landrianlt D, Renaud J F, Zhou X. Occupation times of spectrally negative L6vy processes with applications. Stochastic Processes and Their Applications, 2011, 121(11):2629-2641
[7] Landrianlt D, Renaud J F, Zhou X. An insurance risk model with Parisian implementation delays. Methodology and Computing in Applied Probability, 2014, 16(3):583-607
[8] Lkabous M A, Czarna I, Renaud J F. Parisian ruin for a refracted Levy process. Insurance Mathematics and Economics, 2017, 74:153-163
[9] Kyprianou A E, Loeffen R L. Refracted Lévy processes. Ann Inst H PoincaréProbab Statist, 2010, 46(1):24-44
[10] Renaud J F. On the time spent in the red by a refracted Lévy risk process. Journal of Applied Probability,2013, 51(4):1171-1181
[11] Kyprianou A E. Introductory Lectures on Fluctuations of Levy Processes with Applications. Berlin:Springer, 2006, 42(4):37-57
[12] Loeffen R L, Renaud J F, Zhou X. Occupation times of intervals untill first passage times for spectrally negative Levy processes with applications. Stochastic Processes and Their Applications, 2014, 124(3):1408-1435