Continuous-Time Optimal Portfolio Selection Strategy with Redemption Based on Stochastic Control

In this paper a continuous-time portfolio optimization decision with the redemption is made, a typical portfolio selection model is established by use of Bellman principle of optimality and HJB equation, we derive the optimal strategy and efficient frontier with general stochastic control technique. Its research methodologies can be applied in the practical work such as investment funds management and financial risk management to raise the scientificity of decisions. It is of great referential and inspirational value to provide solutions to practical problem in real investment process.

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Reaching goals under ambiguity: Continuous-time optimal portfolio selection

Statistics & Probability Letters ◽

10.1016/j.spl.2018.01.010 ◽

2018 ◽

Vol 137 ◽

pp. 63-69

Author(s):

Shaolin Ji ◽

Xiaomin Shi

Keyword(s):

Portfolio Selection ◽

Continuous Time ◽

Optimal Portfolio ◽

Time Optimal ◽

Optimal Portfolio Selection

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CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024919500298 ◽

2019 ◽

Vol 22 (06) ◽

pp. 1950029

Author(s):

ZHIPING CHEN ◽

LIYUAN WANG ◽

PING CHEN ◽

HAIXIANG YAO

Keyword(s):

Brownian Motion ◽

Portfolio Selection ◽

Continuous Time ◽

Optimal Strategy ◽

Regime Switching ◽

Efficient Frontier ◽

Defined Contribution ◽

Risky Assets ◽

Mean Variance Portfolio ◽

Mean Variance

Using mean–variance (MV) criterion, this paper investigates a continuous-time defined contribution (DC) pension fund investment problem. The framework is constructed under a Markovian regime-switching market consisting of one bank account and multiple risky assets. The prices of the risky assets are governed by geometric Brownian motion while the accumulative contribution evolves according to a Brownian motion with drift and their correlation is considered. The market state is modeled by a Markovian chain and the random regime-switching is assumed to be independent of the underlying Brownian motions. The incorporation of the stochastic accumulative contribution and the correlations between the contribution and the prices of risky assets makes our problem harder to tackle. Luckily, based on appropriate Riccati-type equations and using the techniques of Lagrange multiplier and stochastic linear quadratic control, we derive the explicit expressions of the optimal strategy and efficient frontier. Further, two special cases with no contribution and no regime-switching, respectively, are discussed and the corresponding results are consistent with those results of Zhou & Yin [(2003) Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model, SIAM Journal on Control and Optimization 42 (4), 1466–1482] and Zhou & Li [(2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization 42 (1), 19–33]. Finally, some numerical analyses based on real data from the American market are provided to illustrate the property of the optimal strategy and the effects of model parameters on the efficient frontier, which sheds light on our theoretical results.

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Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

Abstract and Applied Analysis ◽

10.1155/2014/363046 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14

Author(s):

Hui-qiang Ma

Keyword(s):

Portfolio Selection ◽

Continuous Time ◽

Stock Price ◽

Efficient Frontier ◽

Optimal Portfolio ◽

Portfolio Strategy ◽

Cev Process ◽

The Mean ◽

Mean Variance Portfolio ◽

Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

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