The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected...The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.展开更多
长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度...长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度分析、实地调查验证等方法,识别长春市中心城区城市功能类型。结果表明:单一功能区中,商业功能区数量最多,居住功能区最少;主导—混合功能区中的商业主导功能区及交通主导功能区形成对商业聚集区与轨道交通系统的重要补充;细分—混合功能区特征显示功能混合程度从市中心向周边逐渐加大。经验证,城市功能识别结果符合长春市实际,由此提出对策建议:未来长春市中心城区应注重多中心发展格局,并加强绿地空间和公共服务设施建设。展开更多
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-...We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.展开更多
基金supported by the National Natural science Foundation of china(70271069)
文摘The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.
文摘长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度分析、实地调查验证等方法,识别长春市中心城区城市功能类型。结果表明:单一功能区中,商业功能区数量最多,居住功能区最少;主导—混合功能区中的商业主导功能区及交通主导功能区形成对商业聚集区与轨道交通系统的重要补充;细分—混合功能区特征显示功能混合程度从市中心向周边逐渐加大。经验证,城市功能识别结果符合长春市实际,由此提出对策建议:未来长春市中心城区应注重多中心发展格局,并加强绿地空间和公共服务设施建设。
文摘We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.
