系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2012年
12期
2619~2628
,共null页
保险基金 CEV模型 效用函数 随机控制理论 HJB方程 Legendre变换
保險基金 CEV模型 效用函數 隨機控製理論 HJB方程 Legendre變換
보험기금 CEV모형 효용함수 수궤공제이론 HJB방정 Legendre변환
insurance fund; CEV model; utility function; stochastic optimal control; HJB equation; Legendre transform
假设风险资产价格服从常弹性方差（CEV）模型，保险人面临的风险过程是带漂移的布朗运动．投资过程与承保风险过程完全相关．根据随机最优控制理论，建立保险基金投资问题的HJB方程．由于该方程是非线性偏微分方程，不易求解，因此采用Legendre变换将其转换成对偶问题进行研究．最后针对特定参数值分别得到以CARA和CRRA效用函数为目标的保险人的最优投资策略，这样的投资策略更符合金融市场的实际要求．
假設風險資產價格服從常彈性方差（CEV）模型，保險人麵臨的風險過程是帶漂移的佈朗運動．投資過程與承保風險過程完全相關．根據隨機最優控製理論，建立保險基金投資問題的HJB方程．由于該方程是非線性偏微分方程，不易求解，因此採用Legendre變換將其轉換成對偶問題進行研究．最後針對特定參數值分彆得到以CARA和CRRA效用函數為目標的保險人的最優投資策略，這樣的投資策略更符閤金融市場的實際要求．
가설풍험자산개격복종상탄성방차（CEV）모형，보험인면림적풍험과정시대표이적포랑운동．투자과정여승보풍험과정완전상관．근거수궤최우공제이론，건립보험기금투자문제적HJB방정．유우해방정시비선성편미분방정，불역구해，인차채용Legendre변환장기전환성대우문제진행연구．최후침대특정삼수치분별득도이CARA화CRRA효용함수위목표적보험인적최우투자책략，저양적투자책략경부합금융시장적실제요구．
Research insurance funds investment based on constant elasticity of variance （CEV） model, consider a model which the risky asset is modeled by CEV model and the aggregate claims are modeled by a Brownian motion with drift. As employment of premium is different from ordinary, which means that the insurer should keep an eye on underwrite risk when he use insurance funds, assume that investment risk has a linear correlation with underwrite risk. According to stochastic control theory, derive the HJB equation related with insurance problem. This equation is non-linear partial differential equation, yet it is difficult to solve it, change primary problem to the dual problem by using Legendre transform. Through setting the parameter values, the optimal investment strategy for an insurer with CARA or CRRA utility function is presented and the relevant analysis is given, which provides important practical significance for an insurer to invest.
