A Renewal Shot Noise Process with Subexponential Shot Marks

被引：2
作者：
Chen, Yiqing [1 ]
机构：
[1] Drake Univ, Coll Business & Publ Adm, Des Moines, IA 50311 USA
来源：
RISKS | 2019年 / 7卷 / 02期
关键词：
shot noise; subexponentiality; tail probability; randomly weighted sum; renewal process; LIMIT-THEOREMS; COX PROCESS; TAIL RISK; PORTFOLIO; DRIVEN;
D O I：
10.3390/risks7020063
中图分类号：
F8 [财政、金融];
学科分类号：
0202 ;
摘要：
We investigate a shot noise process with subexponential shot marks occurring at renewal epochs. Our main result is a precise asymptotic formula for its tail probability. In doing so, some recent results regarding sums of randomly weighted subexponential random variables play a crucial role.
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页数：8
相关论文
共 42 条
[1]  
Albrecher H., 2006, SCAND ACTUAR J, V2, P86, DOI DOI 10.1080/03461230600630395
[2]   Tail probabilities for non-standard risk and queueing processes with subexponential jumps [J].
Asmussen, S ;
Schmidli, H ;
Schmidt, V .
ADVANCES IN APPLIED PROBABILITY, 1999, 31 (02) :422-447
[3]   A Cox process with log-normal intensity [J].
Basu, S ;
Dassios, A .
INSURANCE MATHEMATICS & ECONOMICS, 2002, 31 (02) :297-302
[4]  
Bingham N. H., 1989, REGULAR VARIATION
[5]   Power spectra of general shot noises and Hawkes point processes with a random excitation [J].
Brémaud, P ;
Massoulié, L .
ADVANCES IN APPLIED PROBABILITY, 2002, 34 (01) :205-222
[6]   Generalized gamma measures and shot-noise Cox processes [J].
Brix, A .
ADVANCES IN APPLIED PROBABILITY, 1999, 31 (04) :929-953
[7]  
Campbell N, 1910, P CAMB PHILOS SOC, V15, P117
[8]  
Chen Yiqing, 2019, STAT PROBABILITY LET
[9]   Estimation of tail risk based on extreme expectiles [J].
Daouia, Abdelaati ;
Girard, Stephane ;
Stupfler, Gilles .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2018, 80 (02) :263-292
[10]   Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity [J].
Dassios, A ;
Jang, JW .
FINANCE AND STOCHASTICS, 2003, 7 (01) :73-95
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