[01136273]基于Lévy过程的最优分红策略的研究

本成果主要研究含随机投资回报的数学模型及其最优分红策略,把含随机投资回报风险模型中描述的保险风险的基本盈余过程由目前常见的经典风险过程或带干扰的经典风险过程推广为谱负的Levy风险过程或具有某种相关的单边跳跃扩散/更新过程. 系统地研究了破产概率的渐近估计, 上下界; 破产时间, 破产时的赤字和破产前的瞬间盈余三者的联合分布; 模型带分红边界时相关风险分析以及利率及相依关系对破产概率的影响,给出了谱负 Levy 过程的最优分红策略等. 本成果的数学模型及其相关的破产理论和最优分红策略具有重要的理论意义和潜在的应用价值。为保险公司在考虑风险投资时对其业务进行风险评估和科学决策等提供理论参考依据。 主要论文如下： 1、 Yin, Chuancun、Shen, Ying、Wen, Yuzhen,Exit problems for jump processes with applications to dividend problems,Journal of Computational and Applied Mathematics, 245卷, pp 30-52, 2013/6 ,SCI 2、 Yin, Chuancun、Wen, Yuzhen,An extension of Paulsen-Gjessing’’s risk model with stochastic return on investments,Insurance: Mathematics and Economics, 52（3）, pp 469-476, 2013/5 ,SCI 3、 Yin, Chuancun、Wen, Yuzhen,Optimal dividend problem with a terminal value for spectrally positive Levy processes,Insurance: Mathematics and Economics, 53（3）, pp 769-773, 2013/11 ,SCI 4、 Yin, Chuancun、Wen, Yuzhen、Zhao, Yongxia,ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LEVY PROCESS,ASTIN Bulletin, 44（3）, pp 635-651, 2014/9 ,SCI 5、 Yin, Chuancun、Yuen, Kam C.,Exact joint laws associated with spectrally negative Levy processes and applications to insurance risk theory,Frontiers of Mathematics in China, 9（6）, pp 1453-1471, 2014/12,SCI 6、 尹传存、Kam Chuen Yuen,Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs,Journal of Industrial and Management Optimization, 11（4）, pp 1247-1262, 2015/12/15 ,SCI 7、 Yongxia Zhao、Chuancun Yin,The expected discounted penalty function under a renewal risk model with stochastic income,Applied Mathematics and Computation, 218（10）, pp 6144-6154, 2012/1/15 ,SCI 。