Volume 27, 2021
|Number of page(s)||23|
|Published online||20 September 2021|
Multi-time state mean-variance model in continuous time*
Shandong University-Zhong Tai Securities Institute for Financial Studies, Shandong University,
Jinan, PR China.
** Corresponding author: email@example.com
Accepted: 28 August 2021
The objective of the continuous time mean-variance model is to minimize the variance (risk) of an investment portfolio with a given mean at the terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this problem, we consider to minimize the variances of the investment portfolio in the multi-time state. The advantage of this multi-time state mean-variance model is the minimization of the risk of the investment portfolio within the investment period. To obtain the optimal strategy of the model, we introduce a sequence of Riccati equations, which are connected by jump boundary conditions. In addition, we establish the relationships between the means and variances in the multi-time state mean-variance model. Furthermore, we use an example to verify that the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.
Mathematics Subject Classification: 91B28 / 93E20 / 49N10
Key words: Mean-variance / multi-time state / stochastic optimal control
© The authors. Published by EDP Sciences, SMAI 2021
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