Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework

Abstract This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.

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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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Mean-Variance Portfolio Selection with Tracking Error Penalization

Mathematics ◽

10.3390/math8111915 ◽

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

RAIRO - Operations Research ◽

10.1051/ro/2018050 ◽

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.

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

Sba Controle & Automação Sociedade Brasileira de Automatica ◽

10.1590/s0103-17592008000200003 ◽

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.

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

The Scientific World JOURNAL ◽

10.1155/2014/826125 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

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.

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Dynamic Optimal Mean-Variance Portfolio Selection with a 3/2 Stochastic Volatility

Risks ◽

10.3390/risks9040061 ◽

2021 ◽

Vol 9 (4) ◽

pp. 61

Author(s):

Yumo Zhang

Keyword(s):

Stochastic Volatility ◽

Portfolio Selection ◽

Stock Price ◽

Backward Stochastic Differential Equation ◽

Time Inconsistency ◽

Optimal Time ◽

Model Parameters ◽

Mean Variance Portfolio ◽

The Impact ◽

Mean Variance

This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.

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