Abstract: This paper constructs a financial investment model including tradable risk assets,nontradable risk assets and contingent claims under the framework of semimartingale theory. We conduct a study of the exponential utility maximization problem of investment managers' terminal real wealth. The optimal investment strategy and the exact solution of value process with stochastic inflation risk are solved with filter theory, semimartingaleand backward stochastic differential equation theory. According to the results of numerical analysis,the optimal investment amount of tradable risk assets decreases with the increase of expected inflation rate,and the investment value first increases and then decreases. Especially, when the inflation volatility is infinitely close to the nominal price volatility of tradable risk assets,the inflation risk can be fully hedged, and investors will continue to increase the investment in tradable risk assets, in order to maximize the exponential utility of the terminal real wealth. The research results provide a more scientific theoretical reference for the investment decision-making of the financial market.

Key words: stochasticinflation, semimartingale theory, backward stochastic differential equation(BSDE), optimal trading strategy, value process

摘要： 本文在半鞅理论框架下,构建包括可交易风险资产、不可交易风险资产和未定权益的金融投资模型。在考虑随机通胀风险和获取部分市场信息的情形下,研究投资经理人终端真实净财富指数效用最大化问题。运用滤波理论、半鞅和倒向随机微分方程(BSDE)理论,求解带有随机通胀风险的最优投资策略和价值过程精确解。数值分析结果发现,可交易风险资产最优投资额随着预期通胀率的增加而减少,投资价值呈先增后减态势。当通胀波动率无限接近可交易风险资产名义价格波动率时,通胀风险可完全对冲,投资人会不断追加在可交易风险资产的投资额,以期实现终端真实净财富期望指数效用最大化。研究结果为金融市场的投资决策提供更加科学的理论参考。

关键词: 随机通胀, 半鞅理论, 倒向随机微分方程, 最优交易策略, 价值过程