【摘要】：自從Cramer采用隨機過程研究破產(chǎn)問題之后,保險公司的財富優(yōu)化管理問題開始得到了迅速的發(fā)展,其理論不僅充實了金融理論,同時也溝通了金融學(xué)、保險學(xué)與數(shù)學(xué)之間的關(guān)系.對于保險公司來說,最小化破產(chǎn)概率對其發(fā)展有著重要的意義,同時最大化公司財富是管理者的優(yōu)化目標(biāo).論文分別建立盈余過程服從泊松跳躍、復(fù)合泊松跳躍以及盈余過程是Levy過程的數(shù)學(xué)模型,運用鞅方法和隨機控制方法對所建模型的破產(chǎn)概率、最優(yōu)再保險問題以及最優(yōu)投資-再保險問題分別進行研究,得到破產(chǎn)概率、生存概率所滿足的方程以及最優(yōu)投資-再保險策略.主要研究內(nèi)容如下:(1)假定盈余過程帶有泊松跳躍和盈余過程是Levy過程,對保險公司的破產(chǎn)概率進行研究.分別在常利率、隨機利率下以及盈余過程具有Markov調(diào)制參數(shù)時,運用鞅方法和隨機控制的方法得到保險公司的破產(chǎn)概率所滿足的偏微分方程.(2)假定盈余過程帶有泊松跳躍和盈余過程是Levy過程,以最小化破產(chǎn)概率為目標(biāo)對保險公司的再保險問題進行研究.運用鞅方法和隨機控制的方法得到生存概率所滿足的偏微分方程.(3)假定盈余過程帶有泊松跳躍和盈余過程帶有復(fù)合泊松跳躍,以最大化終端財富的期望效用為目標(biāo),對保險公司的最優(yōu)投資-再保險問題進行研究.運用隨機動態(tài)規(guī)劃的方法得到最大化期望指數(shù)效用的最優(yōu)投資-再保險策略.
[Abstract]:Since Cramer used stochastic process to study bankruptcy problem, the optimal wealth management of insurance companies has developed rapidly. Its theory not only enriches financial theory, but also communicates the relationship among finance, insurance and mathematics. For insurance companies, minimizing bankruptcy probability is of great significance to their development, and maximizing corporate wealth is the optimization goal of managers. In this paper, the mathematical models of surplus process from Poisson jump, composite Poisson jump and surplus process are established respectively. The ruin probability of the model is obtained by using martingale method and stochastic control method. The optimal reinsurance problem and the optimal investment-reinsurance problem are studied, and the ruin probability, the equation of survival probability and the optimal investment-reinsurance strategy are obtained. The main contents are as follows: (1) assuming that the earnings process has Poisson jump and the earnings process is the Levy process, the ruin probability of the insurance company is studied. In the case of constant interest rate, random interest rate and the Markov modulation parameter of the earnings process, By using martingale method and stochastic control method, the partial differential equations satisfied by the ruin probability of the insurance company are obtained. (2) it is assumed that the surplus process is Levy process with Poisson jump and earnings process. Aiming at minimizing bankruptcy probability, the reinsurance problem of insurance company is studied. By using martingale method and stochastic control method, the partial differential equations of survival probability are obtained. (3) assuming that the surplus process has Poisson jump and the earnings process has compound Poisson jump, the goal is to maximize the expected utility of the terminal wealth. This paper studies the optimal investment-reinsurance of insurance companies. The optimal investment-reinsurance strategy for maximizing the expected exponential utility is obtained by using stochastic dynamic programming.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：F224;F840.31

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