通过随机控制技术、Bellman最优性原理和HJB方程研究了通货膨胀、随机利率和交易成本等因素影响下的连续时间投资组合选择的最优化问题，将利率假定为服从Vasicek利率模型的随机过程，应用连续时间的动态均值-方差方法得到符合实际意义的HJB方程，通过多重网格的数值逼近方法求解相应的HJB方程得到双目标优化问题的最优投资策略。用实证方法与国内证券市场上代表性指数基金进行对比研究，发现通货膨胀和利率变动以及经济环境和投资者的异质信念等因素均会对最优策略产生影响，有效前沿会随之发生变化，债券与股票之间的投资比例并不是简单维持固定比例就可以保证总资产最优，拓展了基金分离定理。考虑通货膨胀和交易成本等因素的资产组合选择模型可以实实在在为机构投资者提供客观的实践指导和科学的理论依据。
The stochastic control technique, Bellman optimality principle and HJB equations are used to study the optimization of continuous-time portfolio selection under the influence of inflation, stochastic interest rate and transaction cost. The interest rate is assumed to be a stochastic process that obeys the Vasicek interest rate model, a typical HJB equation is established by applying continuous-time dynamic mean-variance approach, the optimal strategy is derived for multi-objective optimization problems with general stochastic control technique and numerical approximation algorithm for multi-grid computing. Using empirical methods to compare with representative index funds in the domestic securities market, it is found that inflation and interest rate changes, as well as economic environment and investors' heterogeneous beliefs, all influence the optimal strategy and change the effective frontier of the portfolio. The ratio between bonds and stocks does not maintain a fixed ratio to ensure that the total assets are optimal, and the fund separation theorem is expanded. The model with inflation and stochastic interest rates is more in line with the actual situation, operational and targeted. The use of nonlinear prediction methods based on support vector machines for time-varying parameter estimation is more conducive to revealing the nature of nonlinear and non-Gaussian distributions in financial markets. The portfolio selection model that considers factors such as inflation and transaction costs can provide institutional investors with a solid theoretical basis and practical guidance.
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