HAL: hal-00165791, version 1

DOI: 10.1016/j.insmatheco.2005.06.004

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Insurance Mathematics and Economics 37, 3 (2005) 421-442

The win-first probability under interest force

Didier Rullière 1, Stéphane Loisel (  Corresponding author ) 1

(2005-12-16)

In a classical risk model under constant interest force, we study the probability that the surplus of an insurance company reaches an upper barrier before a lower barrier. We define this probability as win-first probability. Borrowing ideas from life-insurance theory, hazard rates of the maximum of the surplus before ruin, regarded as a remaining future lifetime random variable, are studied, and provide an original derivation of the win-first probability. We propose an algorithm to efficiently compute this risk-return indicator and its derivatives in the general case, as well as bounds of these quantities. The efficiency of the proposed algorithm is compared with adaptations of other existing methods, and its interest is illustrated by the computation of the expected amount of dividends paid until ruin in a risk model with a dividend barrier strategy.

1:	Laboratoire de Sciences Actuarielle et Financière (SAF)
	Université Claude Bernard - Lyon I : EA2429

Subject

:

Humanities and Social Sciences/Economies and finances Mathematics/Probability

Keyword(s): Ruin probability – hazard rate – upper absorbing barrier – constant interest force – risk-return indicator – win-first probability

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From: Stéphane Loisel <>

Submitted on: Friday, 27 July 2007 15:05:14

Updated on: Wednesday, 1 April 2009 14:35:56