Controlled diffusion models for optimal dividend pay-out

Optimality results for dividend problems in insurance

“…Again it is also possible to use càdlàg controls instead, as is done for constant µ and σ by Asmussen & Taksar [12], see also [111].…”

“…This restricted class of controls is for instance considered in Asmussen & Taksar [12], Jeanblanc-Picqué & Shiryaev [73], Schäl [106] and Gerber & Shiu [55]. In Schmidli [111] the solution of the restricted problem in the Cramér-Lundberg model is shown to converge pointwise to the general solution as l ∞ → ∞.…”

“…In the general diffusion setup the optimal dividend problem (5) was completely solved by Shreve et al [112] and a barrier strategy was identified to be optimal. The special case of constant drift and diffusion coefficient was then solved again by slighty different means in Jeanblanc-Piqué & Shiryaev [73] and Asmussen & Taksar [12] (Radner & Shepp [102] study the situation where the drift and volatility can also be controlled within a discrete set of possible values). In addition to the dividend control, Højgaard & Taksar [68,69] also considered the possibility of proportional reinsurance and optimal investment.…”

“…If one wants to maximize (4) over the set of absolutely continuous controls with a bounded intensity, then a threshold strategy turns out to be optimal in a diffusion risk model (cf. Asmussen & Taksar [12]) as well as in the compound Poisson risk model with exponentially distributed jumps and a < c (cf. Gerber & Shiu [55]).…”

“…for (16) and (20), cf. [12,112]), whereas in other cases it is only possible to prove the existence of a classical solution (e.g. for (17), cf.…”