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On Optimal Periodic Dividend Strategies in the Dual Model with Diffusion

Benjamin Avanzi, University of Montreal - Department of Mathematics and Statistics, University of New South Wales (UNSW) - Australian School of Business - School of Risk and Actuarial Studies
Vincent Tu, University of New South Wales (UNSW) - School of Actuarial Studies
Bernard Wong, University of New South Wales (UNSW) - School of Actuarial Studies


FINANCIAL ENGINEERING eJOURNAL

"On Optimal Periodic Dividend Strategies in the Dual Model with Diffusion" Free Download
Insurance: Mathematics and Economics, Vol. 55C (2014), pp. 210-224

BENJAMIN AVANZI, University of Montreal - Department of Mathematics and Statistics, University of New South Wales (UNSW) - Australian School of Business - School of Risk and Actuarial Studies
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VINCENT TU, University of New South Wales (UNSW) - School of Actuarial Studies
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BERNARD WONG, University of New South Wales (UNSW) - School of Actuarial Studies
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The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.

In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximises the expected present value of dividends paid until ruin. Interestingly, a ‘liquidation-at-first-opportunity’ strategy is optimal in some cases where the surplus processes has a positive drift. Results are illustrated.

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