Zhongfei Li

A minimax portfolio selection strategy with equilibrium

A new minimax model on optimal portfolio selection with uncertainty of both randomness and estimation in inputs is established and the corresponding optimal portfolio is derived analytically. Based on this result, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system under which the total demand and supply of each asset are equal is provided and an explicit formula for such a price system is obtained. Furthermore, some properties of the equilibrium are discussed.

A linear programming algorithm for optimal portfolio selection with transaction costs

We study the optimal portfolio selection problem with transaction costs. In general, the efficient frontier can be determined by solving a parametric non-quadratic programming problem. In a general setting, the transaction cost is a V-shaped function of difference between the existing and the new portfolio. We show how to transform this problem into a quadratic programming model. Hence a linear programming algorithm is applicable by establishing a linear approximation on the utility function of return and variance.

Scalarization and lagrange duality in multiobjective optimization

In this paper, we are concerned with scalarization and the Lagrange duality in multiobjective optimization. After exposing a property of a cone-subconvexlike function, we prove two theorems on scalarization and three theorems of the Lagrange duality.

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.

Mean-CVaR portfolio selection: A nonparametric estimation framework

In this paper, we use Conditional Value-at-Risk (CVaR) to measure risk and adopt the methodology of nonparametric estimation to explore the mean-CVaR portfolio selection problem. First, we obtain the estimated calculation formula of CVaR by using the nonparametric estimation of the density of the loss function, and formulate two nonparametric mean-CVaR portfolio selection models based on two methods of bandwidth selection. Second, in both cases when short-selling is allowed and forbidden, we prove that the two nonparametric mean-CVaR models are convex optimization problems. Third, we show that when CVaR is solved for, the corresponding VaR can also be obtained as a by-product. Finally, we present a numerical example with Monte Carlo simulations to demonstrate the usefulness and effectiveness of our results, and compare our nonparametric method with the popular linear programming method.

Asset-liability management under benchmark and mean-variance criteria in a jump diffusion market

This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the risky asset’s price is governed by an exponential Lévy process, the liability evolves according to a Lévy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.

Multi-period portfolio optimization for asset–liability management with bankrupt control ☆

Abstract In this paper, we investigate a multi-period portfolio optimization problem for asset–liability management of an investor who intends to control the probability of bankruptcy before reaching the end of an investment horizon. We formulate the problem as a generalized mean–variance model that incorporates bankrupt control over intermediate periods. Based on the Lagrangian multiplier method, the embedding technique, the dynamic programming approach and the Lagrangian duality theory, we propose a method to solve the model. A numerical example is given to demonstrate our method and show the impact of bankrupt control and market parameters on the optimal portfolio strategy.

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.

Multi-period mean-variance portfolio selection with stochastic interest rate and uncontrollable liability☆

While the literature on dynamic portfolio selection with stochastic interest rates only confines its investigation to the continuous-time setting up to now, this paper studies a multi-period mean-variance portfolio selection problem with a stochastic interest rate, where the movement of the interest rate is governed by the discrete-time Vasicek model. Invoking dynamic programming approach and the Lagrange duality theory, we derive the analytical expressions for both the efficient investment strategy and the efficient mean-variance frontier of the model formulation. We then extend our model to the situation with an uncontrollable liability.

MODEL RISK IN VaR ESTIMATION: AN EMPIRICAL STUDY

This paper studies the model risk; the risk of selecting a model for estimating the Value-at-Risk (VaR). By considering four GARCH-type volatility processes exponentially weighted moving average (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH), exponential GARCH (EGARCH), and fractionally integrated GARCH (FIGARCH), we evaluate the performance of the estimated VaRs using statistical tests including the Kupiecs likelihood ratio (LR) test, the Christoffersens LR test, the CHI (Christoffersen, Hahn, and Inoue) specification test, and the CHI nonnested test. The empirical study based on Shanghai Stock Exchange A Share Index indicates that both EGARCH and FIGARCH models perform much better than the other two in VaR computation and that the two CHI tests are more suitable for analyzing model risk.