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.

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.

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.

scholarly journals Mean-Variance Portfolio Selection for Defined-Contribution Pension Funds with Stochastic Salary

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Chubing Zhang
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Pension Funds ◽  
Form Solution ◽  
Defined Contribution ◽  
Time Dynamic ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper focuses on a continuous-time dynamic mean-variance portfolio selection problem of defined-contribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.

scholarly journals Multi-Period Mean-Variance Portfolio Selection with Uncertain Time Horizon When Returns Are Serially Correlated

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ling Zhang ◽  
Zhongfei Li
Keyword(s):  
Portfolio Selection ◽  
Optimal Strategy ◽  
Time Horizon ◽  
Optimization Problem ◽  
Exit Time ◽  
Efficient Frontier ◽  
Serial Correlations ◽  
Mean Variance Portfolio ◽  
Uncertain Time ◽  
Mean Variance

We study a multi-period mean-variance portfolio selection problem with an uncertain time horizon and serial correlations. Firstly, we embed the nonseparable multi-period optimization problem into a separable quadratic optimization problem with uncertain exit time by employing the embedding technique of Li and Ng (2000). Then we convert the later into an optimization problem with deterministic exit time. Finally, using the dynamic programming approach, we explicitly derive the optimal strategy and the efficient frontier for the dynamic mean-variance optimization problem. A numerical example with AR(1) return process is also presented, which shows that both the uncertainty of exit time and the serial correlations of returns have significant impacts on the optimal strategy and the efficient frontier.

Provisions for bank deposit withdrawals and portfolio selection

2020 ◽  
Vol 07 (01) ◽  
pp. 1950037
Author(s):  
Ryle S. Perera
Keyword(s):  
Portfolio Selection ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Form Solution ◽  
Investment Portfolio ◽  
Efficient Manner ◽  
Selection For ◽  
Mean Variance Portfolio ◽  
Mean Variance

The primary economic function of a bank is to redirect funds from savers to borrowers in an efficient manner, while increasing the value of the bank’s asset holdings in absolute terms. Within the regulatory framework of the Basel III accord, banks are required to maintain minimum liquidity to guard against withdrawals/liquidity risks. In this paper, we analyze a continuous-time mean-variance portfolio selection for a bank with stochastic withdrawal provisioning by relating the reserves as a proxy for the assets held by the bank. We then formulate an optimal investment portfolio selection for a banker by constructing a special Riccati equation as a continuous solution to the Hamilton–Jacobi–Bellman (HJB) equation under mean-variance paradigm. We obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of the reserve, depository, and intrinsic risk that are associated with the reserve process.

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.

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