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      Optimal Dividend of Compound Poisson Process under a Stochastic Interest Rate

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          Abstract

          In this paper we assume the insurance wealth process is driven by the compound Poisson process. The discounting factor is modelled as a geometric Brownian motion at first and then as an exponential function of an integrated Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of expected discounted dividends up to the time of ruin. We give an explicit expression of the value function and the optimal strategy in the case of interest rate following a geometric Brownian motion. For the case of the Vasicek model, we explore some properties of the value function. Since we can not find an explicit expression for the value function in the second case, we prove that the value function is the viscosity solution of the corresponding HJB equation.

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          Controlled diffusion models for optimal dividend pay-out

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            On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative L\'{e}vy processes

             R. L. Loeffen (2008)
            We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433--443]. Recently Avram, Palmowski and Pistorius [Ann. Appl. Probab. 17 (2007) 156--180] studied the case when the risk process is modeled by a general spectrally negative L\'{e}vy process. We draw upon their results and give sufficient conditions under which the optimal strategy is of barrier type, thereby helping to explain the fact that this particular strategy is not optimal in general. As a consequence, we are able to extend considerably the class of processes for which the barrier strategy proves to be optimal.
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              OPTIMAL REINSURANCE AND DIVIDEND DISTRIBUTION POLICIES IN THE CRAMER-LUNDBERG MODEL

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                Author and article information

                Journal
                20 July 2018
                Article
                1807.08081

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

                Custom metadata
                93E20, 49Lxx
                16 pages, no figures
                q-fin.MF math.OC

                Numerical methods, Quantitative finance

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