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Optimal dividend payout under stochastic discounting

19 novembre 2020 ore 17:00 - 18:00

Aula Luiss Research Seminars, Sede di Luiss

Speaker: Elena Bandini, Università di Milano

We study the optimal dividend problem for a fund manager who aims at maximizing
the flow of dividends discounted according to an interest rate which is
stochastic, and in particular follows a CIR dynamics. The fund income is
modeled as a Brownian motion with drift, and is required to be greater than a
nonnegative minimum capital α. We characterize the value function of the
dividend problem as the unique classical solution of a suitable
Hamilton-Jacobi-Bellman equation. Moreover, we prove that the optimal dividend
strategy is realized by a Skorokhod reflection of the fund value at the optimal
boundary evaluated at the stochastic interest rate. Our results are obtained by
establishing a connection between the dividend problem and a suitable optimal
stopping problem on a diffusion reflected at α and created at a rate
proportional to its local time. The presentation is based on a joint work with
T. De Angelis, G. Ferrari and F. Gozzi.