1,022 research outputs found
Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates
We consider the optimal dividend problem under a habit formation constraint
that prevents the dividend rate to fall below a certain proportion of its
historical maximum, the so-called drawdown constraint. This is an extension of
the optimal Duesenberry's ratcheting consumption problem, studied by Dybvig
(1995) [Review of Economic Studies 62(2), 287-313], in which consumption is
assumed to be nondecreasing. Our problem differs from Dybvig's also in that the
time of ruin could be finite in our setting, whereas ruin was impossible in
Dybvig's work. We formulate our problem as a stochastic control problem with
the objective of maximizing the expected discounted utility of the dividend
stream until bankruptcy, in which risk preferences are embodied by power
utility. We semi-explicitly solve the corresponding Hamilton-Jacobi-Bellman
variational inequality, which is a nonlinear free-boundary problem. The optimal
(excess) dividend rate - as a function of the company's current surplus
and its historical running maximum of the (excess) dividend rate -
is as follows: There are constants such that (1)
for , it is optimal to pay dividends at the lowest
rate , (2) for , it is optimal to
distribute dividends at an intermediate rate , (3)
for , it is optimal to distribute dividends at the
historical peak rate , (4) for , it is optimal to increase
the dividend rate above , and (5) it is optimal to increase via
singular control as needed to keep . Because, the maximum
(excess) dividend rate will eventually be proportional to the running maximum
of the surplus, "mountains will have to move" before we increase the dividend
rate beyond its historical maximum.Comment: To appear in SIAM J. Financial Mathematics, 34 pages, 11 figure
Optimal Investment to Minimize the Probability of Drawdown
We determine the optimal investment strategy in a Black-Scholes financial
market to minimize the so-called {\it probability of drawdown}, namely, the
probability that the value of an investment portfolio reaches some fixed
proportion of its maximum value to date. We assume that the portfolio is
subject to a payout that is a deterministic function of its value, as might be
the case for an endowment fund paying at a specified rate, for example, at a
constant rate or at a rate that is proportional to the fund's value.Comment: To appear in Stochastics. Keywords: Optimal investment, stochastic
optimal control, probability of drawdow
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