1,104 research outputs found
On the Bail-Out Optimal Dividend Problem
This paper studies the optimal dividend problem with capital injection under
the constraint that the cumulative dividend strategy is absolutely continuous.
We consider an open problem of the general spectrally negative case and derive
the optimal solution explicitly using the fluctuation identities of the
refracted-reflected L\'evy process. The optimal strategy as well as the value
function are concisely written in terms of the scale function. Numerical
results are also provided to confirm the analytical conclusions.Comment: To appear in Journal of Optimization Theory and Applications.
Keywords: stochastic control, scale functions, refracted-reflected L\'evy
processes, bail-out dividend proble
Optimal financing and dividend distribution in a general diffusion model with regime switching
We study the optimal financing and dividend distribution problem with
restricted dividend rates in a diffusion type surplus model where the drift and
volatility coefficients are general functions of the level of surplus and the
external environment regime. The environment regime is modeled by a Markov
process. Both capital injections and dividend payments incur expenses. The
objective is to maximize the expectation of the total discounted dividends
minus the total cost of capital injections. We prove that it is optimal to
inject capitals only when the surplus tends to fall below zero and to pay out
dividends at the maximal rate when the surplus is at or above the threshold
dependent on the environment regime
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