On mean-variance portfolio selection under a hidden Markovian regime-switching model

Elliott, Robert J.; Siu, Tak Kuen; Badescu, Alexandru

doi:10.1016/j.econmod.2010.01.007

Cited by 73 publications

(39 citation statements)

References 30 publications

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“…For a hidden Markovian regime-switching diffusion model, Elliott et al [2010] apply, though do not state explicitly, a sufficient maximum principle to a mean-variance portfolio selection problem. However, their model is not the same as the one we consider and hence they do not obtain jumps in the adjoint variables.…”

Section: Introductionmentioning

confidence: 99%

Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

Donnelly

2011

Appl Math Optim

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We prove a sufficient stochastic maximum principle for the optimal control of a regimeswitching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem. . where b n : [0, T ]×R N ×R P ×I → R and σ nm : [0, T ]×R N ×R P ×I → R are given continuous functions for n, m = 1, . . . , N . Using A ⊤ to denote the transpose of a matrix A, set b(t) := (b 1 (t), . . . , b N (t)) ⊤ and σ(t) := (σ nm (t)) N n,m=1 . We consider a performance criterion defined for each x ∈ R N asf (t, X(t), u(t), α(t)) dt + h(X(T ), α(T )) X(0) = x, α(0) = i 0 ,

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Section: Introductionmentioning

confidence: 99%

Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

Donnelly

2011

Appl Math Optim

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“…Bai et al [18,19] develop a bootstrapcorrected estimator to correct the overestimation in portfolio selection and further extend the theory to obtain selffinancing portfolios. Besides, in order to improve the portfolio selection efficiency, researchers tend to extend the models with dynamic programming [13,20,21], with continuous time framework [22,23], using Markovian regime-switching methods [24], and so on.…”

Section: Background Studiesmentioning

confidence: 99%

Portfolio Selection Based on Bayesian Theory

Zhao

Fang

Zhang³

et al. 2019

Mathematical Problems in Engineering

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The traditional portfolio selection model seriously overestimates its theoretic optimal return. Aiming at this problem, two portfolio selection models are proposed to modify the parameters and enhance portfolio performance based on Bayesian theory. Firstly, a Bayesian-GARCH(1,1) model is built. Secondly, Markov Chain is applied to curve the parameters’ state transfer, and a Bayesian Markov regime-Switching-GARCH(1,1) model is constructed. Both the two models can handle the overestimation problem and can obtain self-financing portfolios. In the numerical experiments, both the models are examined with data from China stock market, and their performances are compared and analyzed. The results show that BMS-GARCH(1,1) model is superior to the Bayesian-GARCH(1,1) model.

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“…However, Markowitz states that the mean‐variance criteria dominate the expected utility in the investment practice because of its simplicity in computation and its intuitiveness in the economic explanation of the investment diversification, although Elliott et al . and Bäuerle and Rieder consider the mean‐variance portfolio selection problem with partially observable information in the continuous‐time and discrete‐time setting, respectively. But Bäuerle and Rieder assume that the states of the financial market are completely unobservable, which is far away from the investment practice in the financial market.…”

Section: Introductionmentioning

confidence: 99%

Multi‐period mean variance portfolio selection under incomplete information

Zhang

et al. 2016

Appl Stoch Models Bus & Ind

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This paper solves an optimal portfolio selection problem in the discrete‐time setting where the states of the financial market cannot be completely observed, which breaks the common assumption that the states of the financial market are fully observable. The dynamics of the unobservable market state is formulated by a hidden Markov chain, and the return of the risky asset is modulated by the unobservable market state. Based on the observed information up to the decision moment, an investor wants to find the optimal multi‐period investment strategy to maximize the mean‐variance utility of the terminal wealth. By adopting a sufficient statistic, the portfolio optimization problem with incompletely observable information is converted into the one with completely observable information. The optimal investment strategy is derived by using the dynamic programming approach and the embedding technique, and the efficient frontier is also presented. Compared with the case when the market state can be completely observed, we find that the unobservable market state does decrease the investment value on the risky asset in average. Finally, numerical results illustrate the impact of the unobservable market state on the efficient frontier, the optimal investment strategy and the Sharpe ratio. Copyright © 2016 John Wiley & Sons, Ltd.

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On mean-variance portfolio selection under a hidden Markovian regime-switching model

Cited by 73 publications

References 30 publications

Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

Portfolio Selection Based on Bayesian Theory

Multi‐period mean variance portfolio selection under incomplete information

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