Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1012-1021.

• Articles • Previous Articles     Next Articles

On the Time Value of Ruin for a Renewal Risk Model with Interest

  

  1. (1.School of Mathematics, Qufu Normal University, Shandong Qufu 273165|2.School of Mathematics of Shandong University, Jinan 250100)
  • Received:2007-02-25 Revised:2008-01-30 Online:2009-08-25 Published:2009-08-25
  • Supported by:

    国家自然科学基金(10771119)、山东省自然科学基金(Y2008A12, Y2004A06)、山东省教育厅科研基金(J07yh05)和曲阜师范大学校基金资助

Abstract:

The  paper  studies the ruin problems for a renewal risk model with interest. An integral equation for the Gerber-Shiu discounted penalty function and an explicit infinite series expression for the Gerber-Shiu discounted penalty function are obtained. Then the authors generalize the Gerber-Shiu's formula$^{[4]}$   to this renewal risk process including the force of interest. Finally, as an application of the above results, an
exponential upper bound for the ultimate probability is derived by recursive technique.

Key words: Gerber-Shiu discounted penalty function, Surplus immediately prior to ruin, Deficit at ruin, Discounting factor

CLC Number: 

  • 60J35
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