[Colloquium] [statseminars] Financial Math Seminar: JOSTEIN PAULSEN, Friday, May 9, 2008, 4:30 pm Eckhart 133

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Financial Math Seminar

JOSTEIN PAULSEN
Friday, May 9, 2008
4:30 pm Eckhart 133


Optimal dividend payments and reinvestments of diffusion processes
with both fixed and proportional costs

Assets are assumed to follow a diffusion process subject to some 
conditions. The owners can pay dividends at their discretion, but 
whenever assets reach zero, they have to reinvest money so that assets 
never go negative. With each dividend payment there is a fixed and a 
proportional cost, and so with reinvestments. The goal is to maximize 
expected value of discounted net cash flow, i.e. dividends
paid minus reinvestments. It is shown that there can be two different 
solutions depending on the model parameters and the costs.

1. Whenever assets reach a barrier they are reduced by a fixed amount 
through a dividend payment, and whenever they reach 0 they are increased 
to another fixed amount by a reinvestment.

2. There is no optimal policy, but the value function is approximated by 
policies of the form described in Item 1 for increasing barriers.
We provide criteria to decide whether an optimal solution exists, and 
when not, show how to calculate the value function. It is discussed how 
the problem can be solved numerically and numerial examples are given.

The talk is based on a paper with the same title to appear in SIAM 
Journal of Control and Optimization.
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