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Scandinavian Actuarial Journal Volume 1996, 1996 - Issue 2
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Original Article

On the distribution of the duration of negative surplus

David C. M. Dickson Centre for Actuarial Studies Faculty of Economics and Commerce, University of Melbourne, Parkville 30S2, Victoria, Australia E-mail: [email protected]
&
Alfredo D. Egídio Dos Reis
Pages 148-164 | Received 01 Jan 1995, Published online: 22 Dec 2011

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Ciyu Nie, David C.M. Dickson & Shuanming Li. (2015) The finite time ruin probability in a risk model with capital injections. Scandinavian Actuarial Journal 2015:4, pages 301-318.
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Georgios Psarrakos. (2010) Some results on the joint distribution prior to and at the time of ruin in the classical model. Scandinavian Actuarial Journal 2010:4, pages 268-283.
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Georgios Psarrakos & Konstadinos Politis. (2009) Monotonicity properties and the deficit at ruin in the Sparre Andersen model. Scandinavian Actuarial Journal 2009:2, pages 104-118.
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Georgios Psarrakos & Konstadinos Politis. (2009) A Generalization of the Lundberg Condition in the Sparre Andersen Model and Some Applications. Stochastic Models 25:1, pages 90-109.
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Min Song & Rong Wu. (2007) Total Duration of Negative Surplus for the Risk Process with Constant Interest Force. Stochastic Analysis and Applications 25:6, pages 1263-1272.
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Xiaowen Zhou. (2005) On a Classical Risk Model with a Constant Dividend Barrier. North American Actuarial Journal 9:4, pages 95-108.
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S. N. Chiu & Chuancun Yin. (2002) On occupation times for a risk process with reserve-dependent premium. Stochastic Models 18:2, pages 245-255.
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GordonE. Willmot. (2000) On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin. Scandinavian Actuarial Journal 2000:1, pages 63-79.
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Articles from other publishers (28)

Esther Frostig & Adva Keren–Pinhasik. (2017) Parisian ruin in the dual model with applications to the G/M/1 queue. Queueing Systems 86:3-4, pages 261-275.
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Ye Chen, Yingqiu Li & Xiaowen Zhou. (2017) An occupation time related potential measure for diffusion processes. Frontiers of Mathematics in China 12:3, pages 559-582.
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Lesław Gajek & Łukasz Kuciński. (2017) Complete discounted cash flow valuation. Insurance: Mathematics and Economics 73, pages 1-19.
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Can Jin, Shuanming Li & Xueyuan Wu. (2016) On the occupation times in a delayed Sparre Andersen risk model with exponential claims. Insurance: Mathematics and Economics 71, pages 304-316.
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Hua Dong & Xiang-hua Zhao. (2015) Total duration of negative surplus for a MAP risk model. Applied Mathematics-A Journal of Chinese Universities 30:4, pages 397-406.
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David Landriault & Tianxiang Shi. (2015) Occupation times in the MAP risk model. Insurance: Mathematics and Economics 60, pages 75-82.
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Wei Wang & Jing Min He. (2013) Total duration of negative surplus for a Brownian motion risk model with interest. Acta Mathematica Sinica, English Series 30:1, pages 163-168.
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David C.M. Dickson & Shuanming Li. (2013) The distributions of the time to reach a given level and the duration of negative surplus in the Erlang(2) risk model. Insurance: Mathematics and Economics 52:3, pages 490-497.
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Georgios Psarrakos & Michael Tsatsomeros. (2011) RATIO MONOTONICITY FOR TAIL PROBABILITIES IN THE RENEWAL RISK MODEL. Probability in the Engineering and Informational Sciences 25:2, pages 171-185.
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Ma Xuemin, Yuan Haili & Hu Yijun. (2010) Duration of negative surplus for a two state Markov-modulated risk model. Acta Mathematica Scientia 30:4, pages 1167-1173.
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Jingmin He, Rong Wu & Huayue Zhang. (2009) Total duration of negative surplus for the risk model with debit interest. Statistics & Probability Letters 79:10, pages 1320-1326.
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Min Song, Rong Wu & Xin Zhang. (2008) Total duration of negative surplus for the dual model. Applied Stochastic Models in Business and Industry 24:6, pages 591-600.
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D. V. Husak. (2008) Behavior of risk processes with random premiums after ruin and a multivariate ruin function. Ukrainian Mathematical Journal 59:11, pages 1653-1667.
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D. V. Husak. (2008) Behavior of classical risk processes after ruin and a multivariate ruin function. Ukrainian Mathematical Journal 59:10, pages 1501-1516.
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A. E. Kyprianou & Z. Palmowski. (2016) Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process. Journal of Applied Probability 44:2, pages 428-443.
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Ekaterina T. Kolkovska, José A. López-Mimbela & José Villa Morales. (2005) Occupation measure and local time of classical risk processes. Insurance: Mathematics and Economics 37:3, pages 573-584.
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David C.M. Dickson & Gordon E. Willmot. (2015) The Density of the Time to Ruin in the Classical Poisson Risk Model. ASTIN Bulletin 35:1, pages 45-60.
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F. Avram & M. Usábel. (2015) Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times. ASTIN Bulletin 34:2, pages 315-332.
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Esther Frostig. (2016) Upper bounds on the expected time to ruin and on the expected recovery time. Advances in Applied Probability 36:2, pages 377-397.
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X. Sheldon Lin, Gordon E. Willmot & Steve Drekic. (2003) The classical risk model with a constant dividend barrier: analysis of the Gerber–Shiu discounted penalty function. Insurance: Mathematics and Economics 33:3, pages 551-566.
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David C.M. Dickson & Howard R. Waters. (2014) The Distribution of the time to Ruin in the Classical Risk Model. ASTIN Bulletin 32:2, pages 299-313.
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Alfredo D. Egı́dio dos Reis. (2000) On the moments of ruin and recovery times. Insurance: Mathematics and Economics 27:3, pages 331-343.
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X.Sheldon Lin & Gordon E. Willmot. (2000) The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance: Mathematics and Economics 27:1, pages 19-44.
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X.Sheldon Lin & Gordon E. Willmot. (1999) Analysis of a defective renewal equation arising in ruin theory. Insurance: Mathematics and Economics 25:1, pages 63-84.
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D.C.M. Dickson. (2011) On Numerical Evaluation of Finite Time Survival Probabilities. British Actuarial Journal 5:3, pages 575-584.
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Tomasz Rolski, Hanspeter Schmidli, Volker Schmidt & Jozef Teugels. 1999. Stochastic Processes for Insurance & Finance. Stochastic Processes for Insurance & Finance 617 638 .
Gordon E. Willmot & X. Sheldon Lin. (1998) Exact and approximate properties of the distribution of surplus before and after ruin. Insurance: Mathematics and Economics 23:1, pages 91-110.
Crossref
David C.M. Dickson & Alfredo D. Egídio dos Reis. (1997) The effect of interest on negative surplus. Insurance: Mathematics and Economics 21:1, pages 1-16.
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