## Willmot, Gordon E.

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 Author ID: willmot.gordon-e Published as: Willmot, Gordon E.; Willmot, G. E.; Willmot, Gordon; Willmont, Cordon E.; Willmot, G. more...less External Links: MGP
 Documents Indexed: 104 Publications since 1983, including 8 Books 1 Contribution as Editor Co-Authors: 42 Co-Authors with 80 Joint Publications 728 Co-Co-Authors
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### Co-Authors

 25 single-authored 16 Landriault, David 13 Woo, Jae-Kyung 10 Drekic, Steve 9 Cai, Jun 8 Panjer, Harry H. 6 Klugman, Stuart A. 6 Lin, X. Sheldon 5 Dickson, David C. M. 4 Cheung, Eric C. K. 4 Lin, Xiaodong 3 Feng, Runhuan 3 Lee, Wing Yan 3 Stanford, David A. 3 Xu, Di 2 Kim, Soyeun 2 Li, Bin 2 Pavlova, Kristina P. 2 Shi, Tianxiang 2 Sundt, Bjørn Rosted 2 Tsai, Cary Chi-Liang 1 Cal, Jun 1 Dean, Caron 1 Guo, Ling 1 Hesselager, Ole 1 Huynh, Mirabelle 1 Jones, Bruce L. 1 Kaas, Rob 1 Laeven, Roger J. A. 1 Lemieux, Christiane 1 Lin, Sheldon 1 Liu, Haibo 1 Loke, Sooie-Hoe 1 Moutanabbir, Khouzeima 1 Sprott, David A. 1 Stafford, James E. 1 Tang, Qihe 1 Teugels, Jozef L. 1 Wang, Ruodu 1 Wang, Shaun S. 1 Wei, Yunran 1 Wong, Jeff T. Y. 1 Yang, Hailiang
all top 5

### Serials

 37 Insurance Mathematics & Economics 11 Scandinavian Actuarial Journal 8 Journal of Applied Probability 8 North American Actuarial Journal 7 Scandinavian Actuarial Journal 5 ASTIN Bulletin 4 Wiley Series in Probability and Statistics 3 Advances in Applied Probability 3 Statistics & Probability Letters 2 The Canadian Journal of Statistics 2 Applied Mathematics and Computation 2 Biometrika 2 Operations Research Letters 1 Journal of Econometrics 1 Mathematics of Operations Research 1 Probability in the Engineering and Informational Sciences 1 Methodology and Computing in Applied Probability 1 Applied Stochastic Models in Business and Industry 1 Lecture Notes in Statistics 1 European Actuarial Journal 1 Springer Actuarial 1 Wiley Series in Probability and Mathematical Statistics
all top 5

### Fields

 64 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 59 Statistics (62-XX) 56 Probability theory and stochastic processes (60-XX) 6 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

94 Publications have been cited 1,920 times in 1,150 Documents Cited by Year
Loss models. From data to decisions. 4th revised and updated ed. Zbl 1272.62002
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2012
The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. Zbl 1103.91369
Lin, X. Sheldon; Willmot, Gordon E.; Drekic, Steve
2003
Loss models. From data to decisions. With assistance from: Gary G. Venter. Zbl 0905.62104
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
1998
Loss models: From data to decisions. 3rd ed. Zbl 1159.62070
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2008
Loss models: from data to decisions. Solutions manual. 2nd ed. Zbl 1141.62343
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2004
Analysis of a defective renewal equation arising in ruin theory. Zbl 1028.91556
Lin, X. Sheldon; Willmot, Gordon E.
1999
The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Zbl 0971.91031
Lin, X. Sheldon; Willmot, Gordon E.
2000
A generalized defective renewal equation for the surplus process perturbed by diffusion. Zbl 1074.91563
Tsai, Cary Chi-Liang; Willmot, Gordon E.
2002
On the discounted penalty function in the renewal risk model with general interclaim times. Zbl 1119.91058
Willmot, Gordon E.
2007
Ruin probabilities in the compound binomial model. Zbl 0778.62099
Willmot, Gordon E.
1993
Lundberg approximations for compound distributions with insurance applications. Zbl 0962.62099
Willmot, Gordon E.; Lin, X. Sheldon
2000
Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models. Zbl 1231.91157
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2010
The density of the time to ruin in the classical Poisson risk model. Zbl 1097.62113
Dickson, David C. M.; Willmot, Gordon E.
2005
A mixed Poisson-inverse-Gaussian regression model. Zbl 0679.62051
Dean, C.; Lawless, J. F.; Willmot, G. E.
1989
On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution. Zbl 1152.91591
Landriault, David; Willmot, Gordon
2008
On the expectation of total discounted operating costs up to default and its applications. Zbl 1173.91023
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
The Gerber-Shiu discounted penalty function in the stationary renewal risk model. Zbl 1072.91027
Willmot, Gordon E.; Dickson, David C. M.
2003
The total claims distribution under inflationary conditions. Zbl 0679.62094
Willmot, Gordon E.
1989
On the distribution of the deficit at ruin when claims are phase-type. Zbl 1142.62088
Drekic, Steve; Dickson, David C. M.; Stanford, David A.; Willmot, Gordon E.
2004
Compound geometric residual lifetime distributions and the deficit at ruin. Zbl 1039.62097
Willmot, Gordon E.
2002
The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function. Zbl 1103.91046
Pavlova, Kristina P.; Willmot, Gordon E.
2004
On recursive evaluation of mixed Poisson probabilities and related quantities. Zbl 0796.62094
Willmot, Gordon E.
1993
On the density and moments of the time of ruin with exponential claims. Zbl 1062.60007
Drekic, Steve; Willmot, Gordon E.
2003
Exact and approximate properties of the distribution of surplus before and after ruin. Zbl 0914.90074
Willmot, Gordon E.; Lin, X. Sheldon
1998
On some properties of a class of multivariate Erlang mixtures with insurance applications. Zbl 1390.62092
Willmot, Gordon E.; Woo, Jae-Kyung
2015
Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions. Zbl 1229.91161
Landriault, David; Shi, Tianxiang; Willmot, Gordon E.
2011
Exponential and scale mixtures and equilibrium distributions. Zbl 1076.62559
Hesselager, Ole; Wang, Shaun; Willmot, Gordon E.
1998
Loss models. Further topics. Zbl 1273.62008
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2013
Refinements and distributional generalizations of Lundberg’s inequality. Zbl 0814.62070
Willmot, Gordon E.
1994
Lundberg inequalities for renewal equations. Zbl 1003.60081
Willmot, Gordon E.; Cai, Jun; Lin, X. Sheldon
2001
Loss models. From data to decisions. 5th edition. Zbl 1409.62001
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2019
Equilibrium compound distributions and stop-loss moments. Zbl 1144.91031
Willmot, Gordon E.; Drekic, Steve; Cai, Jun
2005
On the moments of the surplus process perturbed by diffusion. Zbl 1063.91051
Tsai, Cary Chi-Liang; Willmot, Gordon E.
2002
Gerber-Shiu analysis with a generalized penalty function. Zbl 1226.60123
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2010
A note on a class of delayed renewal risk processes. Zbl 1114.60068
Willmot, Gordon E.
2004
A Laplace transform representation in a class of renewal queueing and risk processes. Zbl 0942.60086
Willmot, Gordon E.
1999
Difference equation approaches in evaluation of compound distributions. Zbl 0613.62020
Willmot, G. E.; Panjer, H. H.
1987
On higher-order properties of compound geometric distributions. Zbl 1013.62008
Willmot, Gordon E.
2002
Simplified bounds on the tails of compound distributions. Zbl 0882.60088
Willmot, G. E.; Lin, Xiaodong
1997
Lundberg bounds on the tails of compound distributions. Zbl 0812.60084
Willmot, Gordon E.; Lin, Xiaodong
1994
Further use of Shiu’s approach to the evaluation of ultimate ruin probabilities. Zbl 0675.62075
Willmot, Gordon E.
1988
Statistical independence and fractional age assumptions. With discussion and a reply by the author. Zbl 1080.62549
Willmot, Gordon E.
1997
Asymptotic tail behaviour of Poisson mixtures with applications. Zbl 0696.60085
Willmot, Gordon E.
1990
On the analysis of a general class of dependent risk processes. Zbl 1284.91277
Willmot, Gordon E.; Woo, Jae-Kyung
2012
The compound Poisson surplus model with interest and liquid reserves: Analysis of the Gerber-Shiu discounted penalty function. Zbl 1170.91407
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
Surplus analysis of Sparre Andersen insurance risk processes. Zbl 1391.91006
Willmot, Gordon E.; Woo, Jae-Kyung
2017
On classes of lifetime distributions with unknown age. Zbl 0980.62009
Willmot, Gordon E.; Cai, Jun
2000
On evaluation of the conditional distribution of the deficit at the time of ruin. Zbl 0958.91029
Willmot, Gordon E.
2000
Monotonicity and aging properties of random sums. Zbl 1076.60034
Cai, Jun; Willmot, Gordon E.
2005
On applications of residual lifetimes of compound geometric convolutions. Zbl 1092.62018
Willmot, Gordon E.; Cal, Jun
2004
A remark on the Poisson-Pascal and some other contagious distributions. Zbl 0662.62011
Willmot, Gordon E.
1988
Limiting tail behaviour of some discrete compound distributions. Zbl 0686.62092
Willmot, Gordon E.
1989
The deficit at ruin in the stationary renewal risk model. Zbl 1092.62115
Willmont, Cordon E.; Dikson, David C. M.; Drekic, Steve; Stanford, David A.
2004
On evaluation of the Delaporte distribution and related distributions. Zbl 0721.62019
Willmot, Gordon E.; Sundt, Bjørn
1989
Characterization, robustness, and aggregation of signed Choquet integrals. Zbl 1455.91072
Wang, Ruodu; Wei, Yunran; Willmot, Gordon E.
2020
A note on deficit analysis in dependency models involving Coxian claim amounts. Zbl 1401.91157
Landriault, David; Lee, Wing Yan; Willmot, Gordon E.; Woo, Jae-Kyung
2014
Aging and other distributional properties of discrete compound geometric distributions. Zbl 1025.62006
Willmot, Gordon E.; Cai, Jun
2001
On a partial integrodifferential equation of Seal’s type. Zbl 1318.91124
Willmot, Gordon E.
2015
Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts. Zbl 1231.91250
Willmot, Gordon E.; Woo, Jae-Kyung
2010
Symbolic calculation of the moments of the time of ruin. Zbl 1087.91028
Drekic, Steve; Stafford, James E.; Willmot, Gordon E.
2004
On the moments of the time of ruin with applications to phase-type claims. Zbl 1085.62507
Drekic, Steve; Willmot, Gordon E.
2005
On a class of approximations for ruin and waiting time probabilities. Zbl 0911.90172
Willmot, Gordon E.
1998
A temporal approach to the Parisian risk model. Zbl 1396.60045
Li, Bin; Willmot, Gordon E.; Wong, Jeff T. Y.
2018
On the analysis of a class of loss models incorporating time dependence. Zbl 1280.91149
Guo, Ling; Landriault, David; Willmot, Gordon E.
2013
On the class of Erlang mixtures with risk theoretic applications. Zbl 1480.91253
Willmot, Gordon E.; Woo, Jae-Kyung
2007
Approximations for stop-loss premiums. Zbl 0624.62097
Teugels, Jozef L.; Willmot, G.
1987
Joint moments of the total discounted gains and losses in the renewal risk model with two-sided jumps. Zbl 1427.91077
Cheung, Eric C. K.; Liu, Haibo; Willmot, Gordon E.
2018
On orderings and bounds in a generalized Sparre Andersen risk model. Zbl 1274.60050
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2011
A non-exponential generalization of an inequality arising in queueing and insurance risk. Zbl 0848.60082
Willmot, Gordon E.
1996
A note on the equilibrium M/G/1 queue length. Zbl 0642.60081
Willmot, Gordon E.
1988
On the relationship between bounds on the tails of compound distributions. Zbl 0893.62106
Willmot, Gordon E.
1997
An adaptive premium policy with a Bayesian motivation in the classical risk model. Zbl 1284.91246
Landriault, David; Lemieux, Christiane; Willmot, Gordon E.
2012
Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions. Zbl 0924.62110
Willmot, Gordon E.
1997
On the analysis of time dependent claims in a class of birth process claim count models. Zbl 1304.91118
Landriault, David; Willmot, Gordon E.; Xu, Di
2014
On the construction of a parameter orthogonal to the mean. Zbl 0711.62015
Willmot, Gordon E.
1990
Bounds on the tails of convolutions of compound distributions. Zbl 0853.62082
Willmot, Gordon E.; Lin, Xiaodong
1996
Analysis of the compound Poisson surplus model with liquid reserves, interest and dividends. Zbl 1205.91079
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
Compound Poisson models in actuarial risk theory. Zbl 0525.62097
Panjer, Harry H.; Willmot, Gordon E.
1983
On the transient analysis of the $$M^X/M/\infty$$ queue. Zbl 0991.90040
Willmot, Gordon E.; Drekic, Steve
2001
The preservation of classes of discrete distributions under convolution and mixing. Zbl 1090.60014
Pavlova, Kristina P.; Cai, Jun; Willmot, Gordon E.
2006
On the probabilities of the log-zero-Poisson distribution. Zbl 0632.62012
Willmot, Gordon E.
1987
On posterior probabilities and moments in mixed Poisson processes. Zbl 0711.62093
Willmot, Gordon E.; Sundt, Bjørn
1989
A note on parameters orthogonal to the mean. Zbl 0825.62355
Willmot, G. E.; Sprott, D. A.
1994
The moments of the time to ruin in dependent sparre Andersen models with Coxian claim sizes. Zbl 1401.91161
Lee, Wing Yan; Willmot, Gordon E.
2016
Analysis of IBNR claims in renewal insurance models. Zbl 1402.91205
Landriault, David; Willmot, Gordon E.; Xu, Di
2017
Transient analysis of some infinite server queues. Zbl 1270.60109
Willmot, Gordon E.; Drekic, Steve
2002
On series expansions for scale functions and other ruin-related quantities. Zbl 1447.91142
Landriault, David; Willmot, Gordon E.
2020
The proper distribution function of the deficit in the delayed renewal risk model. Zbl 1277.60142
Kim, So-Yeun; Willmot, Gordon E.
2011
Distributional analysis of a generalization of the Pólya process. Zbl 1231.60077
Willmot, Gordon E.
2010
On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times. Zbl 1306.91079
Lee, Wing Yan; Willmot, Gordon E.
2014
On the joint distributions of the time to ruin, the surplus prior to ruin, and the deficit at ruin in the classical risk model. Zbl 1483.91199
Landriault, David; Willmot, Gordon E.
2009
On a risk model with claim investigation. Zbl 1348.91151
Huynh, Mirabelle; Landriault, David; Shi, Tianxiang; Willmot, Gordon E.
2015
On the analysis of ruin-related quantities in the delayed renewal risk model. Zbl 1348.91158
Kim, So-Yeun; Willmot, Gordon E.
2016
Upper bounds for the tail of the compound negative binomial distribution. Zbl 0888.62105
Willmot, Gordon E.; Lin, Xiaodong
1997
Characterization, robustness, and aggregation of signed Choquet integrals. Zbl 1455.91072
Wang, Ruodu; Wei, Yunran; Willmot, Gordon E.
2020
On series expansions for scale functions and other ruin-related quantities. Zbl 1447.91142
Landriault, David; Willmot, Gordon E.
2020
Loss models. From data to decisions. 5th edition. Zbl 1409.62001
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2019
A temporal approach to the Parisian risk model. Zbl 1396.60045
Li, Bin; Willmot, Gordon E.; Wong, Jeff T. Y.
2018
Joint moments of the total discounted gains and losses in the renewal risk model with two-sided jumps. Zbl 1427.91077
Cheung, Eric C. K.; Liu, Haibo; Willmot, Gordon E.
2018
Surplus analysis of Sparre Andersen insurance risk processes. Zbl 1391.91006
Willmot, Gordon E.; Woo, Jae-Kyung
2017
Analysis of IBNR claims in renewal insurance models. Zbl 1402.91205
Landriault, David; Willmot, Gordon E.; Xu, Di
2017
The moments of the time to ruin in dependent sparre Andersen models with Coxian claim sizes. Zbl 1401.91161
Lee, Wing Yan; Willmot, Gordon E.
2016
On the analysis of ruin-related quantities in the delayed renewal risk model. Zbl 1348.91158
Kim, So-Yeun; Willmot, Gordon E.
2016
On some properties of a class of multivariate Erlang mixtures with insurance applications. Zbl 1390.62092
Willmot, Gordon E.; Woo, Jae-Kyung
2015
On a partial integrodifferential equation of Seal’s type. Zbl 1318.91124
Willmot, Gordon E.
2015
On a risk model with claim investigation. Zbl 1348.91151
Huynh, Mirabelle; Landriault, David; Shi, Tianxiang; Willmot, Gordon E.
2015
A note on deficit analysis in dependency models involving Coxian claim amounts. Zbl 1401.91157
Landriault, David; Lee, Wing Yan; Willmot, Gordon E.; Woo, Jae-Kyung
2014
On the analysis of time dependent claims in a class of birth process claim count models. Zbl 1304.91118
Landriault, David; Willmot, Gordon E.; Xu, Di
2014
On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times. Zbl 1306.91079
Lee, Wing Yan; Willmot, Gordon E.
2014
Loss models. Further topics. Zbl 1273.62008
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2013
On the analysis of a class of loss models incorporating time dependence. Zbl 1280.91149
Guo, Ling; Landriault, David; Willmot, Gordon E.
2013
Loss models. From data to decisions. 4th revised and updated ed. Zbl 1272.62002
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2012
On the analysis of a general class of dependent risk processes. Zbl 1284.91277
Willmot, Gordon E.; Woo, Jae-Kyung
2012
An adaptive premium policy with a Bayesian motivation in the classical risk model. Zbl 1284.91246
Landriault, David; Lemieux, Christiane; Willmot, Gordon E.
2012
Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions. Zbl 1229.91161
Landriault, David; Shi, Tianxiang; Willmot, Gordon E.
2011
On orderings and bounds in a generalized Sparre Andersen risk model. Zbl 1274.60050
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2011
The proper distribution function of the deficit in the delayed renewal risk model. Zbl 1277.60142
Kim, So-Yeun; Willmot, Gordon E.
2011
Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models. Zbl 1231.91157
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2010
Gerber-Shiu analysis with a generalized penalty function. Zbl 1226.60123
Cheung, Eric C. K.; Landriault, David; Willmot, Gordon E.; Woo, Jae-Kyung
2010
Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts. Zbl 1231.91250
Willmot, Gordon E.; Woo, Jae-Kyung
2010
Distributional analysis of a generalization of the Pólya process. Zbl 1231.60077
Willmot, Gordon E.
2010
On the expectation of total discounted operating costs up to default and its applications. Zbl 1173.91023
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
The compound Poisson surplus model with interest and liquid reserves: Analysis of the Gerber-Shiu discounted penalty function. Zbl 1170.91407
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
Analysis of the compound Poisson surplus model with liquid reserves, interest and dividends. Zbl 1205.91079
Cai, Jun; Feng, Runhuan; Willmot, Gordon E.
2009
On the joint distributions of the time to ruin, the surplus prior to ruin, and the deficit at ruin in the classical risk model. Zbl 1483.91199
Landriault, David; Willmot, Gordon E.
2009
Loss models: From data to decisions. 3rd ed. Zbl 1159.62070
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2008
On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution. Zbl 1152.91591
Landriault, David; Willmot, Gordon
2008
On the discounted penalty function in the renewal risk model with general interclaim times. Zbl 1119.91058
Willmot, Gordon E.
2007
On the class of Erlang mixtures with risk theoretic applications. Zbl 1480.91253
Willmot, Gordon E.; Woo, Jae-Kyung
2007
The preservation of classes of discrete distributions under convolution and mixing. Zbl 1090.60014
Pavlova, Kristina P.; Cai, Jun; Willmot, Gordon E.
2006
The density of the time to ruin in the classical Poisson risk model. Zbl 1097.62113
Dickson, David C. M.; Willmot, Gordon E.
2005
Equilibrium compound distributions and stop-loss moments. Zbl 1144.91031
Willmot, Gordon E.; Drekic, Steve; Cai, Jun
2005
Monotonicity and aging properties of random sums. Zbl 1076.60034
Cai, Jun; Willmot, Gordon E.
2005
On the moments of the time of ruin with applications to phase-type claims. Zbl 1085.62507
Drekic, Steve; Willmot, Gordon E.
2005
Loss models: from data to decisions. Solutions manual. 2nd ed. Zbl 1141.62343
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
2004
On the distribution of the deficit at ruin when claims are phase-type. Zbl 1142.62088
Drekic, Steve; Dickson, David C. M.; Stanford, David A.; Willmot, Gordon E.
2004
The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function. Zbl 1103.91046
Pavlova, Kristina P.; Willmot, Gordon E.
2004
A note on a class of delayed renewal risk processes. Zbl 1114.60068
Willmot, Gordon E.
2004
On applications of residual lifetimes of compound geometric convolutions. Zbl 1092.62018
Willmot, Gordon E.; Cal, Jun
2004
The deficit at ruin in the stationary renewal risk model. Zbl 1092.62115
Willmont, Cordon E.; Dikson, David C. M.; Drekic, Steve; Stanford, David A.
2004
Symbolic calculation of the moments of the time of ruin. Zbl 1087.91028
Drekic, Steve; Stafford, James E.; Willmot, Gordon E.
2004
The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function. Zbl 1103.91369
Lin, X. Sheldon; Willmot, Gordon E.; Drekic, Steve
2003
The Gerber-Shiu discounted penalty function in the stationary renewal risk model. Zbl 1072.91027
Willmot, Gordon E.; Dickson, David C. M.
2003
On the density and moments of the time of ruin with exponential claims. Zbl 1062.60007
Drekic, Steve; Willmot, Gordon E.
2003
A generalized defective renewal equation for the surplus process perturbed by diffusion. Zbl 1074.91563
Tsai, Cary Chi-Liang; Willmot, Gordon E.
2002
Compound geometric residual lifetime distributions and the deficit at ruin. Zbl 1039.62097
Willmot, Gordon E.
2002
On the moments of the surplus process perturbed by diffusion. Zbl 1063.91051
Tsai, Cary Chi-Liang; Willmot, Gordon E.
2002
On higher-order properties of compound geometric distributions. Zbl 1013.62008
Willmot, Gordon E.
2002
Transient analysis of some infinite server queues. Zbl 1270.60109
Willmot, Gordon E.; Drekic, Steve
2002
Lundberg inequalities for renewal equations. Zbl 1003.60081
Willmot, Gordon E.; Cai, Jun; Lin, X. Sheldon
2001
Aging and other distributional properties of discrete compound geometric distributions. Zbl 1025.62006
Willmot, Gordon E.; Cai, Jun
2001
On the transient analysis of the $$M^X/M/\infty$$ queue. Zbl 0991.90040
Willmot, Gordon E.; Drekic, Steve
2001
The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Zbl 0971.91031
Lin, X. Sheldon; Willmot, Gordon E.
2000
Lundberg approximations for compound distributions with insurance applications. Zbl 0962.62099
Willmot, Gordon E.; Lin, X. Sheldon
2000
On classes of lifetime distributions with unknown age. Zbl 0980.62009
Willmot, Gordon E.; Cai, Jun
2000
On evaluation of the conditional distribution of the deficit at the time of ruin. Zbl 0958.91029
Willmot, Gordon E.
2000
Analysis of a defective renewal equation arising in ruin theory. Zbl 1028.91556
Lin, X. Sheldon; Willmot, Gordon E.
1999
A Laplace transform representation in a class of renewal queueing and risk processes. Zbl 0942.60086
Willmot, Gordon E.
1999
Loss models. From data to decisions. With assistance from: Gary G. Venter. Zbl 0905.62104
Klugman, Stuart A.; Panjer, Harry H.; Willmot, Gordon E.
1998
Exact and approximate properties of the distribution of surplus before and after ruin. Zbl 0914.90074
Willmot, Gordon E.; Lin, X. Sheldon
1998
Exponential and scale mixtures and equilibrium distributions. Zbl 1076.62559
Hesselager, Ole; Wang, Shaun; Willmot, Gordon E.
1998
On a class of approximations for ruin and waiting time probabilities. Zbl 0911.90172
Willmot, Gordon E.
1998
Simplified bounds on the tails of compound distributions. Zbl 0882.60088
Willmot, G. E.; Lin, Xiaodong
1997
Statistical independence and fractional age assumptions. With discussion and a reply by the author. Zbl 1080.62549
Willmot, Gordon E.
1997
On the relationship between bounds on the tails of compound distributions. Zbl 0893.62106
Willmot, Gordon E.
1997
Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions. Zbl 0924.62110
Willmot, Gordon E.
1997
Upper bounds for the tail of the compound negative binomial distribution. Zbl 0888.62105
Willmot, Gordon E.; Lin, Xiaodong
1997
A non-exponential generalization of an inequality arising in queueing and insurance risk. Zbl 0848.60082
Willmot, Gordon E.
1996
Bounds on the tails of convolutions of compound distributions. Zbl 0853.62082
Willmot, Gordon E.; Lin, Xiaodong
1996
Refinements and distributional generalizations of Lundberg’s inequality. Zbl 0814.62070
Willmot, Gordon E.
1994
Lundberg bounds on the tails of compound distributions. Zbl 0812.60084
Willmot, Gordon E.; Lin, Xiaodong
1994
A note on parameters orthogonal to the mean. Zbl 0825.62355
Willmot, G. E.; Sprott, D. A.
1994
Ruin probabilities in the compound binomial model. Zbl 0778.62099
Willmot, Gordon E.
1993
On recursive evaluation of mixed Poisson probabilities and related quantities. Zbl 0796.62094
Willmot, Gordon E.
1993
Asymptotic tail behaviour of Poisson mixtures with applications. Zbl 0696.60085
Willmot, Gordon E.
1990
On the construction of a parameter orthogonal to the mean. Zbl 0711.62015
Willmot, Gordon E.
1990
A mixed Poisson-inverse-Gaussian regression model. Zbl 0679.62051
Dean, C.; Lawless, J. F.; Willmot, G. E.
1989
The total claims distribution under inflationary conditions. Zbl 0679.62094
Willmot, Gordon E.
1989
Limiting tail behaviour of some discrete compound distributions. Zbl 0686.62092
Willmot, Gordon E.
1989
On evaluation of the Delaporte distribution and related distributions. Zbl 0721.62019
Willmot, Gordon E.; Sundt, Bjørn
1989
On posterior probabilities and moments in mixed Poisson processes. Zbl 0711.62093
Willmot, Gordon E.; Sundt, Bjørn
1989
Further use of Shiu’s approach to the evaluation of ultimate ruin probabilities. Zbl 0675.62075
Willmot, Gordon E.
1988
A remark on the Poisson-Pascal and some other contagious distributions. Zbl 0662.62011
Willmot, Gordon E.
1988
A note on the equilibrium M/G/1 queue length. Zbl 0642.60081
Willmot, Gordon E.
1988
Difference equation approaches in evaluation of compound distributions. Zbl 0613.62020
Willmot, G. E.; Panjer, H. H.
1987
Approximations for stop-loss premiums. Zbl 0624.62097
Teugels, Jozef L.; Willmot, G.
1987
On the probabilities of the log-zero-Poisson distribution. Zbl 0632.62012
Willmot, Gordon E.
1987
Compound Poisson models in actuarial risk theory. Zbl 0525.62097
Panjer, Harry H.; Willmot, Gordon E.
1983
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### Cited by 1,138 Authors

 61 Willmot, Gordon E. 35 Cheung, Eric C. K. 35 Landriault, David 34 Zhang, Zhimin 31 Li, Shuanming 26 Yang, Hailiang 24 Woo, Jae-Kyung 23 Dickson, David C. M. 22 Marceau, Étienne 19 Gómez-Déniz, Emilio 18 Cossette, Hélène 17 Politis, Konstadinos 17 Yang, Hu 16 Albrecher, Hansjörg 16 Cai, Jun 16 Tsai, Cary Chi-Liang 15 Badescu, Andrei L. 15 Lin, X. Sheldon 15 Psarrakos, Georgios 15 Sendova, Kristina P. 14 Brazauskas, Vytaras 14 Drekic, Steve 14 Gerber, Hans U. 13 Calderín Ojeda, Enrique 13 Ren, Jiandong 12 Lu, Yi 12 Wu, Rong 11 Denuit, Michel M. 10 Hürlimann, Werner 10 Landsman, Zinoviy M. 10 Stanford, David A. 10 Yin, Chuancun 10 Yuen, Kam Chuen 9 Feng, Runhuan 9 Sarabia, José María 9 Shiu, Elias S. W. 8 Avram, Florin 8 Bao, Zhenhua 8 Chadjiconstantinidis, Stathis 8 Furman, Edward 8 Guo, Junyi 8 Hu, Yijun 8 Lefèvre, Claude 8 Léveillé, Ghislain 8 Miljkovic, Tatjana 8 Nadarajah, Saralees 8 Szynal, Dominik 8 Valdez, Emiliano A. 8 Wang, Ruodu 7 Ahn, Jae Youn 7 Frostig, Esther 7 Gatto, Riccardo 7 Palmowski, Zbigniew 7 Rabehasaina, Landy 7 Vázquez Polo, Francisco José 7 Xie, Jiehua 7 Zou, Wei 6 Antonio, Katrien 6 Bhati, Deepesh 6 Constantinescu, Corina D. 6 Egídio dos Reis, Alfredo D. 6 Frees, Edward W. 6 Hu, Xiang 6 Jones, Bruce L. 6 Kim, Joseph Hyun Tae 6 Li, Bin 6 Vernic, Raluca 6 Zitikis, Ričardas 5 Cha, Ji Hwan 5 Gajek, Lesław 5 Hernández-Bastida, Agustin 5 Hong, Liang 5 Jang, Jiwook 5 Karlis, Dimitris 5 Kim, Bara 5 Lee, Wing Yan 5 Liu, Zaiming 5 Makov, Udi E. 5 Papaioannou, Apostolos D. 5 Pitts, Susan M. 5 Šiaulys, Jonas 5 Su, Jianxi 5 Sundt, Bjørn Rosted 5 Thonhauser, Stefan 5 Verbelen, Roel 5 Wu, Xueyuan 5 Xu, Di 5 Young, Virginia R. 4 Adékambi, Franck 4 Ahmad, Zubair 4 Ahn, Soohan 4 Badía, Francisco German 4 Bee, Marco 4 Beirlant, Jan 4 Boucher, Jean-Philippe 4 Chen, Mi 4 Chi, Yichun 4 Dean, Charmaine B. 4 Finkelstein, Maxim 4 Gao, Jianwei ...and 1,038 more Authors
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### Cited in 144 Serials

 297 Insurance Mathematics & Economics 109 Scandinavian Actuarial Journal 86 North American Actuarial Journal 50 Communications in Statistics. Theory and Methods 42 Journal of Computational and Applied Mathematics 42 Statistics & Probability Letters 39 Methodology and Computing in Applied Probability 37 ASTIN Bulletin 25 Applied Mathematics and Computation 24 Journal of Applied Probability 17 European Actuarial Journal 14 Stochastic Models 13 Acta Mathematicae Applicatae Sinica. English Series 13 Queueing Systems 12 Communications in Statistics. Simulation and Computation 12 Journal of Statistical Computation and Simulation 10 Journal of Applied Statistics 10 Probability in the Engineering and Informational Sciences 9 Lithuanian Mathematical Journal 9 Scandinavian Actuarial Journal 9 Applied Stochastic Models in Business and Industry 8 Computational Statistics and Data Analysis 8 Applied Mathematics. Series B (English Edition) 8 Journal of Industrial and Management Optimization 7 Journal of Statistical Planning and Inference 7 Journal of the Korean Statistical Society 6 European Journal of Operational Research 6 Lobachevskii Journal of Mathematics 5 Advances in Applied Probability 5 Operations Research Letters 5 Statistical Papers 5 Journal of Mathematical Sciences (New York) 5 Lifetime Data Analysis 5 Modern Stochastics. Theory and Applications 4 Metrika 4 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 4 Annals of Operations Research 4 Applicationes Mathematicae 4 Extremes 4 Acta Mathematica Sinica. English Series 4 Advances in Difference Equations 4 Journal of Statistical Theory and Practice 3 Journal of Mathematical Analysis and Applications 3 Physica A 3 Annals of the Institute of Statistical Mathematics 3 Stochastic Analysis and Applications 3 Mathematical and Computer Modelling 3 Computational Statistics 3 Stochastic Processes and their Applications 3 Mathematical Problems in Engineering 3 Finance and Stochastics 3 Mathematical Methods of Operations Research 3 Stochastics 3 Frontiers of Mathematics in China 3 The Annals of Applied Statistics 2 Automatica 2 Biometrical Journal 2 Biometrics 2 Journal of Econometrics 2 Journal of Multivariate Analysis 2 Mathematics and Computers in Simulation 2 Mathematics of Operations Research 2 Siberian Mathematical Journal 2 Acta Applicandae Mathematicae 2 Bulletin of the Iranian Mathematical Society 2 Computers & Operations Research 2 The Annals of Applied Probability 2 Applied Mathematical Modelling 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Abstract and Applied Analysis 2 International Journal of Theoretical and Applied Finance 2 International Journal of Modern Physics C 2 Journal of Systems Science and Complexity 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Asia-Pacific Financial Markets 2 Statistical Methodology 2 Statistics and Computing 2 Dependence Modeling 2 Journal of Statistical Distributions and Applications 1 The Canadian Journal of Statistics 1 Discrete Applied Mathematics 1 International Journal of Systems Science 1 Ukrainian Mathematical Journal 1 Theory of Probability and its Applications 1 International Statistical Review 1 Metron 1 Statistica 1 Applied Mathematics and Mechanics. (English Edition) 1 Acta Mathematica Hungarica 1 Statistics 1 Applied Mathematics Letters 1 Economics Letters 1 Japan Journal of Industrial and Applied Mathematics 1 International Journal of Computer Mathematics 1 SIAM Review 1 Statistische Hefte 1 Indagationes Mathematicae. New Series 1 Tatra Mountains Mathematical Publications 1 Test 1 SIAM Journal on Scientific Computing ...and 44 more Serials
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### Cited in 29 Fields

 810 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 618 Statistics (62-XX) 542 Probability theory and stochastic processes (60-XX) 40 Numerical analysis (65-XX) 36 Operations research, mathematical programming (90-XX) 28 Integral equations (45-XX) 21 Systems theory; control (93-XX) 17 Integral transforms, operational calculus (44-XX) 11 Computer science (68-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Partial differential equations (35-XX) 4 Special functions (33-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Real functions (26-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Geophysics (86-XX) 2 Mathematics education (97-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX)