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Total duration of negative surplus for the risk model with debit interest

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  • He, Jingmin
  • Wu, Rong
  • Zhang, Huayue

Abstract

This paper investigates the compound Poisson risk model with debit interest. The model assumes that the company is allowed to borrow at some debit interest rate when the surplus turns negative. We obtain the Laplace-Stieltjes transform (LST) of the hitting time of the risk process with constant interest when the initial value is less than the hitting level. By the LST together with the strong Markov property of the model, we obtain the LST of the total duration of negative surplus.

Suggested Citation

  • He, Jingmin & Wu, Rong & Zhang, Huayue, 2009. "Total duration of negative surplus for the risk model with debit interest," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1320-1326, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:10:p:1320-1326
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    References listed on IDEAS

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    1. Picard, Philippe, 1994. "On some measures of the severity of ruin in the classical Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 14(2), pages 107-115, May.
    2. Kolkovska, Ekaterina T. & Lopez-Mimbela, Jose A. & Morales, Jose Villa, 2005. "Occupation measure and local time of classical risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 573-584, December.
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    4. Egidio dos Reis, Alfredo, 1993. "How long is the surplus below zero?," Insurance: Mathematics and Economics, Elsevier, vol. 12(1), pages 23-38, February.
    5. Gerber, Hans U., 1990. "When does the surplus reach a given target?," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 115-119, September.
    6. Gerber, Hans U. & Shiu, Elias S. W., 1997. "The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 129-137, November.
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    Cited by:

    1. Ming, Rui-Xing & Wang, Wen-Yuan & Xiao, Li-Qun, 2010. "On the time value of absolute ruin with tax," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 67-84, February.

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