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      On the optimal dividend problem for a spectrally negative L\'{e}vy process

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          Abstract

          In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative L\'{e}vy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.

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          Author and article information

          Journal
          28 February 2007
          Article
          10.1214/105051606000000709
          math/0702893
          Custom metadata
          60J99 (Primary) 93E20, 60G51 (Secondary)
          IMS-AAP-AAP403
          Annals of Applied Probability 2007, Vol. 17, No. 1, 156-180
          Published at http://dx.doi.org/10.1214/105051606000000709 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
          math.PR q-fin.PR
          vtex

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