scholarly journals Continuous time mean–variance–utility portfolio problem and its equilibrium strategy

Optimization ◽  
2021 ◽  
pp. 1-29
Author(s):  
Ben-Zhang Yang ◽  
Xin-Jiang He ◽  
Song-Ping Zhu
Keyword(s):  
Continuous Time ◽  
Equilibrium Strategy ◽  
Portfolio Problem ◽  
Mean Variance

Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth

2021 ◽  
Author(s):  
Xue Dong He ◽  
Zhaoli Jiang
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Weighted Average ◽  
Equilibrium Strategy ◽  
Aspiration Level ◽  
Return Rates ◽  
Terminal Wealth ◽  
Instantaneous Change ◽  
Mean Variance Portfolio ◽  
Mean Variance

In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of the agent’s terminal wealth must exceed a target and minimize the variance of the agent’s terminal wealth. The agent can revise the expected terminal wealth target dynamically to adapt to the change of the agent’s current wealth, and we consider the following three targets: (i) the agent’s current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent’s current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent’s current wealth and a preset aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of the agent’s wealth subject to a certain constraint on the expectation of the instantaneous change of the agent’s wealth.

scholarly journals Multi-time state mean-variance model in continuous time

2021 ◽  
Vol 27 ◽  
pp. 92
Author(s):  
Shuzhen Yang
Keyword(s):  
Boundary Conditions ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Investment Portfolio ◽  
Variance Model ◽  
Investment Plan ◽  
Terminal Time ◽  
Variance Risk ◽  
Maximum Drawdown ◽  
Mean Variance

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.

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