部分信息实物投资的消费效用无差别定价

Consumption utility-based pricing of the option to invest with partial information

运用滤波理论,随机控制理论和消费效用无差别定价原理,建立基于部分信息的非完备市场有对冲机会的实物投资回报一次性支付的期权定价模型.通过求解具有自由边界条件的高维偏微分方程,推导出期权的隐含价值和投资最优执行边界,确定了投资,消费及资产分配的最优决策,并详细讨论了投资回报波动风险,平均回报率估计偏差风险以及资产相关系数对实物期权的隐含价值以及隐含信息价值的影响.模型和结论对实物投资项目的估值和资产管理具有一定参考价值.

By filter theory, stochastic control theory and consumption utility indifference pricing method, we conduct a real investment model of lump-sum payoff with hedging opportunities in an incomplete market with partial information. By solving a three-dimensional free-boundary partial differential equation （PDE）, we obtain the implied value of the option to invest and investment threshold, and identify the optimal investment, consumption decision and portfolio selection. Then we discuss the impacts of changes in the volatility of the investment, the mean appreciation rate estimation risk, and the correlation on the implied value of the option to invest and the implied information value. Our paper has some reference value for an estimation of a real investment and asset management in practice.