Optimal dividend policies for a class of growth-restricted di usion processes under transaction costs and solvency constraints
Peer reviewed, Journal article
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Original versionFinance and Stochastics 16(3): 477-511 https://doi.org/10.1007/s00780-011-0169-5
In this paper, we consider a company where surplus follows a rather general di usion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment there are transaction costs and taxes and it is shown in  that under some reasonable assumptions, optimality is achieved by using a lump sum dividend barrier strategy, i.e. there is an upper barrier u and a lower barrier u so that whenever surplus reaches u , it is reduced to u through a dividend payment. However, these optimal barriers may be unacceptably low from a solvency point of view. It is argued that in that case one should still we should look for a barrier strategy, but with barriers that satisfy a given constraint. We propose a solvency constraint similar to that in ; whenever dividends are paid out the probability of ruin within a xed time T and with the same strategy in the future, should not exceed a predetermined level ". It is shown how optimality can be achieved under this constraint, and numerical examples are given.