Spring 2009 Wednesday, April 22   Speaker: Jostein Paulson Department of Mathematics University of Bergen, Norway Title: Optimal dividend policies for a general class of diffusions with transaction costs and solvency constraints" Abstract: We consider a company where surplus follows a rather general diffusion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment there are transaction costs and taxes. We will recapitulate a result of Paulsen (2007), where it is shown 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 look for a barrier strategy, but with barriers that satisfy the given constraints. We propose a solvency constraint similar to that in Paulsen (2003); whenever dividends are paid out the probability of ruin within a fixed time T and with the same strategy in the future, should not exceed a predetermined level ε. It is shown how optimality can be achieved under this constraint, and numerical examples are given.

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