Xili Zhang

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.

An optimization model of the portfolio adjusting problem with fuzzy return and a SMO algorithm

Based on possibilistic mean and variance theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exist transaction costs in portfolio adjusting precess. We propose a portfolio optimization model with V-shaped transaction cost which is associated with a shift from the current portfolio to an adjusted one. A sequential minimal optimization (SMO) algorithm is developed for calculating the optimal portfolio adjusting strategy. The algorithm is based on deriving the shortened optimality conditions for the formulation and solving 2-asset sub-problems. Numerical experiments are given to illustrate the application of the proposed model and the efficiency of algorithm. The results also show clearly the influence of the transaction costs in portfolio selection.

Maximum-likelihood estimators in the mixed fractional Brownian motion

This paper deals with the problem of estimating the parameters for the mixed fractional Brownian motion from discrete observations based on the maximum-likelihood method. The asymptotic properties, namely consistency and asymptotic normality, are presented for these estimates. By adapting the optimization algorithm, these two estimates can be efficiently computed by the computer software. The performance of the maximum-likelihood method is tested on simulated mixed fractional Brownian motion data sets, and is compared with the approach proposed by Filatova [Mixed fractional Brownian motion: Some related questions for computer network traffic modelling, International Conference on Signals and Electronic Systems, Kraków, Poland, 2008, pp. 393–396].

Parameter identification for the discretely observed geometric fractional Brownian motion

This paper deals with the problem of estimating all the unknown parameters of geometric fractional Brownian processes from discrete observations. The estimation procedure is built upon the marriage of the quadratic variation and the maximum likelihood approach. The asymptotic properties of the estimators are provided. Moveover, we compare our derived method with the approach proposed by Misiran et al. [Fractional Black-Scholes models: complete MLE with application to fractional option pricing. In International conference on optimization and control; Guiyang, China; 2010. p. 573–586.], namely the complete maximum likelihood estimation. Simulation studies confirm theoretical findings and illustrate that our methodology is efficient and reliable. To show how to apply our approach in realistic contexts, an empirical study of Chinese financial market is also presented.

Degeneracy Resolution for Bilinear Utility Functions

Loss-aversion is a phenomenon where investors are particularly sensitive to losses and eager to avoid them. An efficient method to solve the portfolio optimization problem of maximizing the bilinear utility function is given by Best et al. (Loss-Aversion with Kinked Linear Utility Functions, CORR 2010-04, University of Waterloo, 2010). This method is useful because it performs its computations only using asset related quantities rather than much higher dimensional quantities of the LP formulation. However, a difficulty with this method is that it requires a nondegeneracy assumption which may not be satisfied. This paper implements Bland’s least-index rules to the method in such a way that the efficiency of the method is retained. Then we describe the numerical results of applying our algorithm to a series of six asset problems in which the degree of loss-aversion is increased.

Parameter Identification for Drift Fractional Brownian Motions with Application to the Chinese Stock Markets

This article deals with the problem of estimating all the unknown parameters in the drift fractional Brownian motion with discretely sampled data. The estimation procedure is built upon the marriage of the variation method and the ergodic theory. The strong consistencies of these estimators are provided. Moreover, our method and two existing approaches are compared based on the computational running time and the accuracy of estimation via simulation studies. We also apply the proposed method to the real high-frequency financial data within a window of 4 h in the trading day from the Chinese mainland stock market.

Modeling the Dynamics of Shanghai Interbank Offered Rate Based on Single-Factor Short Rate Processes

Using the Shanghai Interbank Offered Rate data of overnight, 1 week, 2 week and 1 month, this paper provides a comparative analysis of some popular one-factor short rate models, including the Merton model, the geometric Brownian model, the Vasicek model, the Cox-Ingersoll-Ross model, and the mean-reversion jump-diffusion model. The parameter estimation and the model selection of these single-factor short interest rate models are investigated. We document that the most successful model in capturing the Shanghai Interbank Offered Rate is the mean-reversion jump-diffusion model.