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.
LI Ai-zhong, WANG Shou-yang, PENG Yue-lan
. Continuous-time Asset Allocation Strategy with Inflation and Stochastic Interest Rates[J]. Chinese Journal of Management Science, 2019
, 27(2)
: 61
-70
.
DOI: 10.16381/j.cnki.issn1003-207x.2019.02.007
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