认股权证的修正精算定价研究

基于修正Bladt和Rydberg在无市场假设下关于期权定价的保险精算方法的基础上,从评估实际损失和相应概率分布角度,利用公平保费原则建立认股权证的定价模型,并给出定价公式.且当投资者对原生资产期望回报率为无风险利率时,该定价为风险中性价格.     

私募基金管理者的收益定价、风险选择与契约设计

考虑到市场非完备和私募基金管理者风险厌恶的实际情形,本文根据效用无差别原理,得到基金管理者收益的确定性等价价值满足的偏微分方程,并运用有限差分法进行数值分析.结果表明:非系统风险溢价的增大使得收益价值与自有资金率呈递增但呈边际递减规律;管理者的风险选择决定于非系统风险和风险厌恶态度,在契约有限期的情形下,风险中性型管理者会选择无限大的基金波动率,风险厌恶程度低(高)的管理者会选择尽可能大(小)的基金波动率;并从确定性等价的角度讨论了契约设计问题.     

Risk Measure and Premium Distribution on Catastrophe Reinsurance

In this paper, we propose a new risk measure which is based on the Orlicz premium principle to characterize catastrophe risk premium. The intention is to develop a formulation strategy for Catastrophe Fund. The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer, and the differential earnings between the reinsurance premium and the reinsurer's retention is accumulated as a part of Catastrophe Fund. We demonstrate that the aforementioned risk measure has some good properties, which are further confirmed by numerical simulations in R environment.     

二元混合型指数分布的识别性及其应用

对新提出的一类二元混合型指数分布和其他三类二元混合型指数分布,讨论了它们的分布识别问题,即记z=min（x1,x2）,I=i,当z=xi;记U-max（＆,x2）,J=j,当U=Xi;已知（Z,I）或（U,J）的分布,求（X1,X2）分布的唯一性问题．给出了（x1,x2）服从Marshall-Olkin型指数分布时,有关寿险中Z及u的精算现值的2个公式．     

随机利率下的终身寿险

本文给出 了 在 随机 利率下,终身寿 险的纯保费和 纯保 费责任准备金的计算方 法.并讨论了与之 有关的其他精算 问题.     

保费随机收取的双险种二项风险模型的破产概率

本文考虑双险种二项风险模型,对保单到达时收取的保费是一随机变量进行了研究,得到了其破产概率的一般公式和lundberg不等式.     

人寿保险中的最优缴费模型

精算数学中 ,将自然保费制转化为现今的均衡保费制 ,精算师并未考虑投保人的最优缴费策略 .本文采用最优化方法对定期寿险保单的缴费方式进行了分析 .得出 ,当精算师计算保费的利息与“银行储蓄利率”相等时 ,均衡收缴保费是保险人的最优策略 ,否则应分别采用递增或递减缴费策略 .     

Analytical best upper bounds on stop-loss premiums

We provide a list of best upper bounds on the stop-loss premium E(X?t)₊ corresponding to the risk X and the retention limit t. Various information (moments, unimodality, symmetry,…) on the distribution F of X is taken into account.     

Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit

In most studies on optimal reinsurance, little attention has been paid to controlling the reinsurer’s risk. However, real-world insurance markets always place a limit on coverage, otherwise the insurer will be subjected to under a heavy financial burden when the insured suffers a large unexpected covered loss. In this paper, we revisit the optimal reinsurance problem under the optimality criteria of VaR and TVaR risk measures when the constraints for the reinsurer’s risk exposure are presented. Two types of constraints are considered that have been proposed by Cummins and Mahul (2004) and Zhou et al. (2010), respectively. It is shown that two-layer reinsurance is always the optimal reinsurance policy under both VaR and TVaR risk measures and under both types of constraints. This implies that the two-layer reinsurance policy is more robust. Furthermore, the optimal quantity of ceded risk depends on the confidence level, the safety loading and the tolerance level, as well as on the relation between them.