Mathematics – Optimization and Control
Scientific paper
2011-06-14
Mathematics
Optimization and Control
Key Words: Piecewise-deterministic compound Poisson model, optimal stochastic control, HJB equation, quasi-variational inequal
Scientific paper
This paper deals with optimal dividend payment problem in the general setup of a piecewise-deterministic compound Poisson risk model. The objective of an insurance business under consideration is to maximize the expected discounted dividend payout up to the time of ruin. Both restricted and unrestricted payment schemes are considered. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding Hamilton-Jacobi-Bellman equation, which, in turn, leads to an optimal restricted dividend payment policy. When the claims are exponentially distributed, the value function and an optimal dividend payment policy of the threshold type are determined in closed forms under certain conditions. The case of unrestricted payment scheme gives rise to a singular stochastic control problem. By solving the associated integro-differential quasi-variational inequality, the value function and an optimal barrier strategy are determined explicitly in exponential claim size distributions. Two examples are demonstrated and compared to illustrate the main results.
Feng Runhuan
Zhang Shuaiqi
Zhu Chao
No associations
LandOfFree
Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114251