سیاست تقسیم سود مطلوب برای فرآیندهای ترکیب پواسون: مورد نرخ تقسیم سود محدود
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|46064||2012||17 صفحه PDF||سفارش دهید||18437 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Insurance: Mathematics and Economics, Volume 51, Issue 1, July 2012, Pages 26–42
We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg model with arbitrary claim-size distribution. Our objective is to find the dividend payment policy which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy imposing a ceiling on the dividend rates. We characterize the optimal value function as the unique bounded viscosity solution of the associated Hamilton–Jacobi–Bellman equation. We prove that there exists an optimal dividend strategy and that this strategy is stationary with a band structure. We study the regularity of the optimal value function. We find a characterization result to check optimality even in the case where the optimal value function is not differentiable. We construct examples where the claim-size distribution is smooth but the optimal dividend policy is not threshold and the optimal value function is not differentiable. We study the survival probability of the company under the optimal dividend policy. We also present examples where the optimal dividend policy has infinitely many bands even in the case that the claim-size distribution has a bounded density.