跳跃扩散过程下企业的最优投资策略  

Optimal Investment Strategy under Jump-diffusion Processes

作　　者：刘彦云 胡支军 LIU Yan-yun;HU Zhi-jun(School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025

出　　处：《重庆工商大学学报（自然科学版）》2021年第4期73-83,共11页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：越来越多的不确定因素使得投资企业很难快速决策以抓住最佳投资时机从而获取最大收益。针对这一问题,假定项目投资成本和产出价格均不确定且受突发事件的影响,通过建立不确定因素服从跳跃扩散过程的实物期权模型,求解了企业的投资期权价值和投资阈值,并分析了最相关参数对企业投资阈值的影响。在以往文献假设不确定因素相互独立的基础上,考虑了不确定因素的随机波动之间具有相关性的情形;在保留突发事件引起的跳跃幅度随机分布的假设框架下,运用均值、波动率、偏度3个统计特征参数对突发事件进行了刻画,进而推广了比较静态结果。研究结果表明:投资成本和产出价格的波动相关性越大,投资阈值越小,企业的最优投资策略为加快执行投资期权;而且,投资成本和产出价格的随机波动率对投资阈值的影响不仅与自身有关,而且取决于它们的相对波动率与相关性之间的大小关系;此外,引起投资阈值波动的主要因素是跳跃幅度均值和偏度而不是标准差,因此企业在作出投资策略前应重点考察突发事件的性质和影响方向。More and more uncertain factors make it difficult for investment enterprises to make quick decisions and seize the best investment opportunity to obtain the maximum revenue.Aiming at this problem,this paper assumes that both the project’s investment cost and output price are not only uncertain but also affected by shocks,establishes a real option model under which uncertain factors follow the jump-diffusion processes,solves the optimal investment threshold and the optimal investment option value,as well as analyzes the impact of the most relevant parameters on the optimal investment threshold.Based on the assumption that the uncertain factors are independent of each other in the previous literature,we relax the assumption of the statistical independence between the the volatility of two uncertain factors.In the framework of the hypothesis of random distribution of jump amplitude,this paper uses the three statistical characteristic parameters,namely,mean value,volatility and skewness,to describe the shocks and generalize the comparative static results.The results show that,the greater the volatility correlation between the investment cost and the output price,the smaller the investment threshold,and the firm’s corresponding optimal investment strategy is to accelerate the execution of investment options.Moreover,the influence of random volatility of investment cost and output price on investment threshold is not only related to itself,but also depends on the relationship between their relative volatility and correlation,meanwhile,the main factors that cause the fluctuation of investment threshold are the mean and skewness of jump amplitude rather than the standard deviation.Therefore,the firms should focus on the nature and influence direction of shocks before making investment strategies.

关 键 词：跳跃扩散过程 投资期权 投资阈值 最优策略 相关性 

分 类 号：O224[理学—运筹学与控制论]