On optimal periodic dividend strategies in the dual model with diffusion

Lévy insurance risk process with Poissonian taxation

“…the model dynamics of the taxed surplus process still follows X θ with the time of ruin now defined by τ c θ = inf {t > 0 : X θ t < 0}. Such a model assumption can be viewed as a complement to risk processes with periodic dividend barrier strategy and continuous monitoring of solvency, which were studied by Avanzi et al (2013Avanzi et al ( , 2014, Zhang (2014) and Zhang & Cheung (2014a, 2014b. In addition, one can also treat the present model as the reverse case of Albrecher & Ivanovs (2014, Section 6), which is concerned with Poissonian monitoring of ruin but continuous checking for tax payments.…”

“…A taxation system with delayed tax payment is also studied. In Section 4, we consider the situation where solvency is monitored continuously, but tax is still payable at Poissonian time points (see Avanzi et al (2013Avanzi et al ( , 2014, Zhang (2014) and Zhang & Cheung (2014a, 2014b for similar assumptions in dividend problems), and results analogous to those in Section 3 can readily be obtained. Section 5 ends the paper with some numerical illustrations.…”

On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

“…For the case without capital injections in which dividends are paid until the time of ruin, a periodic barrier strategy that pays any excess above a certain barrier at each payment opportunity is expected to be optimal. Its optimality has been confirmed for the spectrally positive Lévy (dual) models by Avanzi et al [3] and Pérez and Yamazaki [15], and for the spectrally negative Lévy models with a completely monotone Lévy density by Noba et al [14]. On the other hand, Optimal periodic dividend and capital injection strategies 1273 regarding the bail-out case, the optimality results are available only for the dual model given in the second problem considered in [15], to the best of the authors' knowledge.…”

Double continuation regions for American options under Poisson exercise opportunities

“…Several related stochastic control problems have been analyzed under the same Poisson observation settings. See Avanzi et al (2014), Avanzi et al (2013), and Noba et al (2018) for the optimal dividend problem and Palmowski et al (2020) for determining the endogenous bankruptcy level.…”