2021/10/18 by Kei Noba, Noba, Kei
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Advanced Queuing Theory Analysis #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2110.09560
openalex publication_date 2021/10/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we study de Finetti's optimal dividend problem with capital\ninjection under the assumption that the dividend strategies are absolutely\ncontinuous. In many previous studies, the process before being controlled was\nassumed to be a spectrally one-sided L 'evy process, however in this paper we\nuse a L 'evy process that may have both positive and negative jumps. In the\nmain theorem, we show that a refraction--reflection strategy is an optimal\nstrategy. We also mention the existence and uniqueness of solutions of the\nstochastic differential equations that define refracted L 'evy processes.\n