CAJ | 학술논문

本文研究CEV模型下基于效用最大化的资产-负债管理问题。文章假设股票价格服从CEV模型，而负债服从带漂移的布朗运动，且与股票价格存在一般相关性。应用动态规划原理得到值函数满足的HJB方程，并应用Legendre变换-对偶方法得到其对偶方程。假设投资人对风险的偏好满足二次效用函数，并应用变量替换方法得到最优投资组合的闭式解。结果表明：最优投资组合包含一个修正因子，该修正因子可影响投资人为对冲波动率风险而作出的投资决策。最后，文章分析了修正因子的性质并考察了修正因子对最优投资组合的影响。
본문연구CEV모형하기우효용최대화적자산-부채관리문제。문장가설고표개격복종CEV모형，이부채복종대표이적포랑운동，차여고표개격존재일반상관성。응용동태규화원리득도치함수만족적HJB방정，병응용Legendre변환-대우방법득도기대우방정。가설투자인대풍험적편호만족이차효용함수，병응용변량체환방법득도최우투자조합적폐식해。결과표명：최우투자조합포함일개수정인자，해수정인자가영향투자인위대충파동솔풍험이작출적투자결책。최후，문장분석료수정인자적성질병고찰료수정인자대최우투자조합적영향。
In this paper, we consider an asset and liability management problem under the utility maximizing criterion, in which stock price is assumed to comply with the constant elasticity of variance (CEV) model, while liability follows the Brownian motion with drift, and liability and stock price are generally correlated between each other. We apply the dynamic programming principle to solving the HJB equation for the value function and use the Legendre transform-dual technique to transform the HJB equation into its dual equation. Furthermore, we choose a quadratic utility function for our analysis and obtain the closed-form solution to the optimal portfolio by applying the variable change approach. The result indicates that the optimal portfolio includes a modified factor which is capable of reflecting an investor’s decision to hedge the volatility risk. Finally, we analyze the property of the modified factor and investigate its effect on the optimal portfolio.