MULTI-PERIOD MEAN-VARIANCE PORTFOLIO SELECTION WITH MARKOV REGIME SWITCHING AND UNCERTAIN TIME-HORIZON

This paper investigates a multi-period mean-variance portfolio selection with regime switching and uncertain exit time. The returns of assets all depend on the states of the stochastic market which are assumed to follow a discrete-time Markov chain. The authors derive the optimal strategy and the efficient frontier of the model in closed-form. Some results in the existing literature are obtained as special cases of our results.

AN INEXACT PROXIMAL DC ALGORITHM FOR THE LARGE-SCALE CARDINALITY CONSTRAINED MEAN-VARIANCE MODEL IN SPARSE PORTFOLIO SELECTION

Optimization problem of cardinality constrained mean-variance(CCMV)model for sparse portfolio selection is considered.To overcome the difficulties caused by cardinality constraint,an exact penalty approach is employed,then CCMV problem is transferred into a difference-of-convex-functions(DC)problem.By exploiting the DC structure of the gained problem and the superlinear convergence of semismooth Newton(ssN)method,an inexact proximal DC algorithm with sieving strategy based on a majorized ssN method(siPDCA-mssN)is proposed.For solving the inner problems of siPDCA-mssN from dual,the second-order information is wisely incorporated and an efficient mssN method is employed.The global convergence of the sequence generated by siPDCA-mssN is proved.To solve large-scale CCMV problem,a decomposed siPDCA-mssN(DsiPDCA-mssN)is introduced.To demonstrate the efficiency of proposed algorithms,siPDCA-mssN and DsiPDCA-mssN are compared with the penalty proximal alternating linearized minimization method and the CPLEX(12.9)solver by performing numerical experiments on realword market data and large-scale simulated data.The numerical results demonstrate that siPDCA-mssN and DsiPDCA-mssN outperform the other methods from computation time and optimal value.The out-of-sample experiments results display that the solutions of CCMV model are better than those of other portfolio selection models in terms of Sharp ratio and sparsity.

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.

Mean-variance Portfolio Selections in Continuous-time Model with Stochastic Interest Rate Process

Under the continuous time （d＋1） assets market model with finite time horizon T, and the condition that all coefficients in model are stochastic processes, the decision of investment portfolio selection had been studied. By using K.Itǒ formuia and backward stochastic differential equation＇s theory, on the relation of investment portfolio processes, fortune processes, the backward stochastic differential equation model for stochastic control problem had been established, the relation between the prime fortune process and the end- all fortune process had been proposed, the existence and uniqueness of investment portfolio had been proved, and the formula for investment portfolio had been arrived. On the setting of mean-variance portfolio selection, we obtained the formula of optimal efficient investment portfolio. Furthermore, the mean-variance efficient frontier is too obtained explicitly in the form of parameter.

AN UTILITIES BASED APPROACH FOR MULTI-PERIOD DYNAMIC PORTFOLIO SELECTION

This paper proposed a multi-period dynamic optimal portfolio selection model. Assumptions were made to assure the strictness of reasoning. This Approach depicted the developments and changing of the real stock market and is an attempt to remedy some of the deficiencies of recent researches. The model is a standard form of quadratic programming. Furthermore, this paper presented a numerical example in real stock market.

Time Consistent Multi-period Worst-Case Risk Measure in Robust Portfolio Selection

In this paper,we first construct a time consistent multi-period worst-case risk measure,which measures the dynamic investment risk period-wise from a distributionally robust perspective.Under the usually adopted uncertainty set,we derive the explicit optimal investment strategy for the multi-period robust portfolio selection problem under the multi-period worst-case risk measure.Empirical results demonstrate that the portfolio selection model under the proposed risk measure is a good complement to existing multi-period robust portfolio selection models using the adjustable robust approach.

The Impact of General Correlation Under Multi-Period Mean-Variance Asset-Liability Portfolio Management

This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.

Liquidity risk integration in portfolio choice： The bid efficient frontier

In this paper, a tractable solution is proposed to integrate, to a certain extent, market liquidity risk in the portfolio selection process. It is shown how an investor may take advantage of this additional risk source within the standard mean-variance optimization framework, by in certain circumstances overcoming the pitfalls of illiquidity and in others seizing a liquidity premium. Bid prices appear effective to capture liquidity risk. The efficient frontier conceived with bid prices consists of mean-variance optimal allocations that cover more liquid stocks （large caps） under stressed market conditions and less liquid stocks （small caps） under normal conditions.

Mean-Field Maximum Principle for Optimal Control of Forward–Backward Stochastic Systems with Jumps and its Application to Mean-Variance Portfolio Problem

We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.

OPTIMAL MULTI-ASSET INVESTMENT WITH NO-SHORTING CONSTRAINT UNDER MEAN-VARIANCE CRITERION FOR AN INSURER

This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic （LQ） control theory with no-shorting constraint. Then the efficient strategy （optimal investment strategy） and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman （HJB） equation.

A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.

Maximum Principle of Optimal Stochastic Control with Terminal State Constraint and Its Application in Finance

This paper considers the optimal control problem for a general stochastic system with general terminal state constraint. Both the drift and the diffusion coefficients can contain the control variable and the state constraint here is of non-functional type. The author puts forward two ways to understand the target set and the variation set. Then under two kinds of finite-codimensional conditions, the stochastic maximum principles are established, respectively. The main results are proved in two different ways. For the former, separating hyperplane method is used; for the latter, Ekeland＇s variational principle is applied. At last, the author takes the mean-variance portfolio selection with the box-constraint on strategies as an example to show the application in finance.