存在违约风险时的最优资产组合  

Optimal Portfolio with Default Risk

作　　者：卞世博[1] 刘海龙[2] 

机构地区：[1]上海立信会计学院风险管理研究院,上海201620 [2]上海交通大学安泰经济与管理学院,上海200052

出　　处：《管理工程学报》2012年第3期28-33,共6页Journal of Industrial Engineering and Engineering Management

基　　金：上海市教育委员会科研创新项目(12YS154)

摘　　要：本文研究了当存在违约风险时,一个代表性投资者投资于一个可违约债券、股票以及银行存款的最优资产配置问题。利用简约化模型来刻画可违约债券的违约风险,并给出其价格的动态过程。通过随机控制方法给出了此优化问题的解析解。结果表明跳跃(违约)风险的存在,使可违约债券的最优投资策略不再是连续函数。当可违约债券违约时,投资者对可违约债券的持有量为零;当债券未发生违约时,投资者对可违约债券的最优持有量主要受信用利差、违约强度以及投资期限的影响。In the ＂classical＂ optimal portfolio literature, only market risk or cognitive risk associated with market is considered. In spite of their several major contributions to the theory of optimal asset selection only a handful of papers consider the case where one or more of the securities in the portfolio are subject to default risk. These authors use a diversification argument implying that jump risk do not show up in well-diversified portfolios of defaultable bonds and the impact of jump risk on portfolio management cannot be studied. In this paper we research a representative investor on how she optimally allocated her wealth among the following securities： a defaultable bond, a stock and a bank account. Because we assume that the investor invests a defaultable bond, there is jump risk in defauhable bond. Bring the jump risk into the investment portfolio is key innovation of this paper. We adopt the reduced-form approach to model the defaultable bond, and give the dynamics of defaultable bond. If the investor＇s utility is CRRA and stochastic control methods are adopted, we can obtain closed form solutions for the optimal strategies. The optimal strategy for the stock is constant irrespective of pre-default or post-default. The reason is that the stock has no correlation with the defaultable bond, which means there is no need to hedge for the default. Thus the optimal strategy for the stock is invariant to the default risk. The optimal strategy for the stock depends on the risk aversion, the market price of risk for the stock and the coefficient of the volatility of the stock return. Assume that the utility function is CRRA, the optimal strategy for the stock is independent of the investment horizon, so-called ＂myopic＂ effect. The optimal strategy of the defaultable bond is not a continuous function because of jump risk. The value of the defauhable bond after default is assumed to be zero. Thus, the post-defauh optimal strategy for defaultable bond is zero. The pre-default optimal strategy for defao

关 键 词：违约风险 简约化模型 最优资产组合 随机控制 

分 类 号：F731[经济管理—产业经济]