scholarly journals Multi-period mean-variance portfolio optimization with markov switching parameters

2008 ◽  
Vol 19 (2) ◽  
pp. 138-146
Author(s):  
Oswaldo L. V. Costa ◽  
Michael V. Araujo
Keyword(s):  
Optimal Control ◽  
Portfolio Selection ◽  
Regime Switching ◽  
Efficient Frontier ◽  
Control Policy ◽  
Control Law ◽  
Numerical Examples ◽  
Markov Random ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper we deal with a multi-period mean-variance portfolio selection problem with the market parameters subject to Markov random regime switching. We analytically derive an optimal control policy for this mean-variance formulation in a closed form. Such a policy is obtained from a set of interconnected Riccati difference equations. Additionally, an explicit expression for the efficient frontier corresponding to this control law is identified and numerical examples are presented.

Mean-variance portfolio selection with an uncertain exit-time in a regime-switching market

2019 ◽  
Vol 53 (4) ◽  
pp. 1171-1186
Author(s):  
Reza Keykhaei
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Exit Time ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Homogeneous Markov Chain ◽  
Investment Strategies ◽  
Special Cases ◽  
Mean Variance Portfolio ◽  
Mean Variance

In this paper, we deal with multi-period mean-variance portfolio selection problems with an exogenous uncertain exit-time in a regime-switching market. The market is modelled by a non-homogeneous Markov chain in which the random returns of assets depend on the states of the market and investment time periods. Applying the Lagrange duality method, we derive explicit closed-form expressions for the optimal investment strategies and the efficient frontier. Also, we show that some known results in the literature can be obtained as special cases of our results. A numerical example is provided to illustrate the results.

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

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.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

scholarly journals Mean-Variance Portfolio Selection with Tracking Error Penalization

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1915
Author(s):  
William Lefebvre ◽  
Grégoire Loeper ◽  
Huyên Pham
Keyword(s):  
Portfolio Selection ◽  
Tracking Error ◽  
Efficient Frontier ◽  
Minimum Variance ◽  
Sharpe Ratio ◽  
Portfolio Strategy ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Variance Criterion

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

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