基于破产概率的保险投资策略和保费定价

发布时间：2018-06-22 00:08

本文选题：随机控制 + HJB方程　；参考：《福州大学》2013年硕士论文

【摘要】：在金融数学和保险数学的范畴内,破产理论是风险理论的核心内容。保险公司作为经营风险的特殊机构,在经营过程中也会有各种风险,因此对其自身经营风险的研究极为重要。为了提高保险公司的偿付能力,确保其稳定运作,科学地预测保险公司未来的保费收入、可能发生的理赔额以及估计保险公司的破产概率等,都是十分重要的课题。在保险公司的经营过程中,一方面要将保费收入用于投资以获得利润收益,另一方面要预留一部分资金以备索赔的支付。预留资金过少增大了经营风险,投资结构不合理又影响资金效率。我们将从破产概率的角度考量这一问题,为保险公司的投资决策提供便利。在经典复合泊松模型中,保险公司将资金投入一个风险投资过程和一个无风险投资过程。当索赔的分布确定后,运用随机控制中的HJB方程最小化保险公司的破产概率,在已知投资规模或投资组合的情况下求解二者中的另一项,进而利用数值算法得到最优投资策略并讨论各种策略的运用对破产概率的影响,避免了求解高阶微分积分方程的困难。该课题解决保险公司的投资资金分配问题,在实际应用中具有一定的参考价值。在最后一章中,我们通过对Cramer-Lundberg模型的修改,将保费收入改为复合泊松过程,使其更好地吻合实际。通过带有两个复合泊松过程的破产模型,估计破产概率,推导出保费的计算公式,尤其是针对指数分布的情形。该方法可以用于指导保险公司对各险种定价,并发现保险公司通过提高保费或扩大规模来减小破产概率的做法并不有效。
[Abstract]:In the category of financial mathematics and insurance mathematics, bankruptcy theory is the core content of risk theory. As a special organization of management risk, insurance company also has all kinds of risks in the course of operation, so it is very important to study its own management risk. In order to improve the solvency of insurance companies and ensure their stable operation, it is very important to scientifically predict the future premium income of insurance companies, the amount of claims that may occur and estimate the bankruptcy probability of insurance companies. In the course of operation of insurance company, on the one hand, premium income should be invested to gain profits, on the other hand, some funds should be set aside for payment of claims. Too little reserve funds increase the risk of operation, and the unreasonable structure of investment affects the efficiency of funds. We will consider this from the perspective of bankruptcy probability to facilitate the investment decision of insurance companies. In the classical compound Poisson model, the insurance company puts the capital into a venture capital investment process and a risk free investment process. When the distribution of claims is determined, the HJB equation in stochastic control is used to minimize the ruin probability of the insurance company. Furthermore, the optimal investment strategy is obtained by numerical algorithm and the influence of various strategies on ruin probability is discussed, which avoids the difficulty of solving higher order differential integral equations. This subject solves the problem of investment fund allocation of insurance company, and has certain reference value in practical application. In the last chapter, by modifying the Cramer-Lundberg model, we change the premium income into a compound Poisson process to make it more consistent with the practice. Based on the ruin model with two complex Poisson processes, the ruin probability is estimated and the formula for calculating the premium is derived, especially for the exponential distribution. This method can be used to guide insurance companies to price each insurance, and it is found that it is not effective for insurance companies to reduce the probability of bankruptcy by increasing the premium or expanding the scale.
【学位授予单位】：福州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F840

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