TY - JOUR A2 - Wang, Guangchen AU - Li, Yan AU - Liu, Guoxin PY - 2015 DA - 2015/03/22 TI - Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model SP - 439537 VL - 2015 AB - We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model. The value function V(x) is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin. It is shown that V(x) can be characterized by the Hamilton-Jacobi-Bellman equation. We find the optimal dividend barrier b, the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier -z*. In the case of exponential claim size especially, we give an explicit procedure to obtain b, -z*, and the value function V(x). SN - 1024-123X UR - https://doi.org/10.1155/2015/439537 DO - 10.1155/2015/439537 JF - Mathematical Problems in Engineering PB - Hindawi Publishing Corporation KW - ER -