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      A multidimensional problem of optimal dividends with irreversible switching: a convergent numerical scheme

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          Abstract

          In this paper we study the problem of optimal dividend payment strategy which maximizes the expected discounted sum of dividends to a multidimensional set up of n associated insurance companies where the surplus process follows an n-dimensional compound Poisson process. The general manager of the companies has the possibility at any time to exercise an irreversible switch into another regime; we also take into account an expected discounted value at ruin. This multidimensional dividend problem is a mixed singular control/optimal problem. We prove that the optimal value function is a viscosity solution of the associated HJB equation and that it can be characterized as the smallest viscosity supersolution. The main contribution of the paper is to provide a numerical method to approximate (locally uniformly) the optimal value function by an increasing sequence of sub-optimal value functions of admissible strategies defined in an n-dimensional grid. As a numerical example, we present the optimal time of merger for two insurance companies.

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

          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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            On the Time Value of Ruin

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              OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMER-LUNDBERG MODEL

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                Author and article information

                Journal
                07 April 2018
                Article
                1804.02547

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                math.OC math.NA

                Numerical & Computational mathematics, Numerical methods

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