一类投资时点问题的最优停止模型及其等待时间  

OPTIMAL STOPPING MODEL AND WAITING TIME OF PROBLEMS OF INVESTMENT TIMING

作　　者：黄薇[1] 张宗益[2] 

机构地区：[1]重庆大学数理学院,重庆400030 [2]重庆大学经济与工商管理学院,重庆400030

出　　处：《系统科学与数学》2009年第2期242-252,共11页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(70571089);教育部新世纪优秀人才(NCET-07-0905)项目资助.

摘　　要：针对收益流与一次性投入沉淀成本均不确定的一类风险项目,为使其预期总的贴现净收益最大,提出了寻找项目最优投资时点的最优停止模型.这种方法不依赖于金融市场的完备性及市场无套利.借助于高切原理,通过求解一个自由边界问题,得到模型的候选解.运用最优停止理论证明了其的确为最优解,从而显式地给出了该类风险项目的最优投资时点.进一步,显式给出了到达最优时点的平均等待时间.When cash flows and sunk cost of a class of risky projects both uncontrollable and stochastic, optimal investment timing for the projects are modeled with optimal stopping. This approach dose not require assumption of complete market or no-arbitrage. In terms of the well-known ＂high contact ＂principle a candidate solution of the model is obtained by solving a free boundary problem. The optimality of the candidate solution is proven by optimal stopping theory. So the optimal investment timing is given explicitly for the objective of maximizing the expected total discounted net profit. Finally the mean waiting time to optimal investment timing is given explicitly.

关 键 词：最优停止 投资时点 高切原理 Ito扩散 平均等待时间. 

分 类 号：O224[理学—运筹学与控制论] O226[理学—数学]