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.

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.

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.

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.

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.

scholarly journals A Closed-Form Solution for Robust Portfolio Selection with Worst-Case CVaR Risk Measure

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Le Tang ◽  
Aifan Ling
Keyword(s):  
Portfolio Selection ◽  
Risk Measure ◽  
Closed Form Solution ◽  
Efficient Frontier ◽  
Form Solution ◽  
Var Model ◽  
Numerical Comparison ◽  
Worst Case ◽  
Robust Portfolio ◽  
Robust Portfolio Selection

With the uncertainty probability distribution, we establish the worst-case CVaR (WCCVaR) risk measure and discuss a robust portfolio selection problem with WCCVaR constraint. The explicit solution, instead of numerical solution, is found and two-fund separation is proved. The comparison of efficient frontier with mean-variance model is discussed and finally we give numerical comparison with VaR model and equally weighted strategy. The numerical findings indicate that the proposed WCCVaR model has relatively smaller risk and greater return and relatively higher accumulative wealth than VaR model and equally weighted strategy.

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

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.

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.

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