In this paper, we study optimal dividend problems in a diffusion risk model for two different cases depending on whether reinsurance is incorporated. In either case, the dividend rate is bounded above by a constant, and the company earns investment income at a constant force of interest. Unlike existing approaches in the literature dealing with optimal problems with interest, we allow the force of interest to be greater than the discount factor, and we use a different method to solve the corresponding Hamilton–Jacobi–Bellman (HJB) equation instead of introducing a confluent hypergeometric function. We conclude that the optimal dividend policy is of a threshold type and show that the corresponding dividend barrier is nondecreasing in the dividend rate bound. In cases where there is no reinsurance, we construct an auxiliary reflecting control problem to find the nonzero dividend barrier. If proportional reinsurance is purchased, the optimal reinsurance strategy looks somewhat strange. The optimal retention level of risk first increases monotonically with risk reserve to some possible value (less than $$1$$ 1 ) and then stays at level $$1$$ 1 for a while or, if $$1$$ 1 has been reached, finally, it decreases to 0.
Applied Mathematics and Optimization – Springer Journals
Published: Feb 1, 2016
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera