跳-扩散市场环境下基于CEV模型的最优再保险-投资问题研究

发布时间：2018-05-15 02:23

本文选题：跳--扩散模型 + 偿债率模型　；参考：《安徽工程大学》2017年硕士论文

【摘要】：随着金融市场的完善,各企业合理地规避风险和进行市场投资成为了其核心内容,其中通过保险公司进行投保,是目前企业中最常见用来降低金融风险的方法之一,因此可见保险公司在当今社会中所占的地位越来越重要.而保险公司作为一个盈利机构,也处于金融市场当中,也面临着众多的金融风险.保险公司如何降低自身风险和合理投资成为了金融领域的重点研究内容之一.本文首先通过引入对保险公司偿债率模型的了解,逐步展开研究.当保险公司处于金融困境成本时,考虑在分数布朗环境下,建立带随机利率的保险商偿债率(SR)模型.通过测度变换理论得到新的风险中性测度,并利用分数布朗环境下的欧式看涨期权的定价公式,得到保险公司最终收益的贴现值.其次,在对保险公司初步理解的基础之上,我们开始研究关于保险公司最优再保险--投资策略.其中基于A-C情形下的盈余模型,利用指数效用函数使得保险公司终端财富最大化,通过随机控制理论,得到相应策略的显示表达式,并采用数值模拟方式,进一步分析了各参数的影响情况.最后,我们考虑了在带有期权且满足CEV模型的风险市场下,通过超额损失再保险的方式,研究了相应的最优策略.利用指数效用函数,以保险公司终端财富最大化为目标,应用随机控制理论,求解出相应的最优再保险-投资策略.并通过数值模型来进一步说明最优策略与相关参数的关系.
[Abstract]:With the perfection of the financial market, it is the core content of various enterprises to avoid risks and invest in the market reasonably. Insurance through insurance companies is one of the most common methods used to reduce financial risks in enterprises at present. Therefore, it can be seen that the status of insurance companies in today's society is becoming more and more important. As a profitable institution, insurance companies are also faced with numerous financial risks in the financial market. Insurance companies how to reduce their own risk and reasonable investment has become one of the key research content in the financial field. In this paper, first of all, by introducing the understanding of the insurance company debt-paying rate model, step-by-step research. When the insurance company is in financial distress, the SRR model with stochastic interest rate is established in the fractional Brown environment. A new risk-neutral measure is obtained by means of the measure transformation theory. By using the pricing formula of the European call option in fractional Brown environment, the present value of the insurance company's final return is obtained. Secondly, based on the preliminary understanding of insurance companies, we begin to study the optimal reinsurance-investment strategy of insurance companies. Based on the earnings model in A-C case, the exponential utility function is used to maximize the terminal wealth of the insurance company. Through the stochastic control theory, the display expression of the corresponding strategy is obtained, and the numerical simulation method is adopted. The influence of each parameter is further analyzed. Finally, we consider the risk market with option and satisfy CEV model, and study the optimal strategy by means of excess loss reinsurance. By using exponential utility function and aiming at maximizing the terminal wealth of insurance companies, the optimal reinsurance and investment strategy is solved by using stochastic control theory. The relationship between the optimal strategy and the related parameters is further explained by numerical model.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F842.3

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