Weilin Xiao

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.

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].

A fuzzy portfolio selection method based on possibilistic mean and variance

This paper deals with the portfolio selection problem when the returns of assets obey LR-type possibility distributions and there exist the limits on holdings. A new possibilistic mean–variance model to portfolio selection is proposed based on the definitions of the possibilistic return and possibilistic risk, which can better integrate an uncertain decision environment with vagueness and ambiguity. This possibilistic mean–variance model can be regarded as extensions of conventional probabilistic mean–variance methodology and previous possibilistic approaches since it contains less parameter and has a more extensive application. A numerical example of a possibilistic fuzzy portfolio selection problem is given to illustrate our proposed effective means and approaches.

Modeling Chinese stock returns with stable distribution

In this paper we demonstrate that an @a-stable distribution is better fitted to Chinese stock return data in the Shanghai Composite Index and the Shenzhen Component Index than the classical Black-Scholes model. The sample quantile method developed by McCulloch [J.H. McCulloch, Simple consistent estimators of stable distribution parameters, Communications in Statistics-Simulation and Computation 15 (4) (1986) 1109-1136] is used to estimate the @a-stable distribution for the Shanghai Composite Index and the Shenzhen Component Index. The empirical results show that the asymmetric leptokurtic features presented in the Shanghai Composite Index and Shenzhen Component Index returns can be captured by an @a-stable law.

Is It Reasonable for Saaty's Consistency Test in the Pairwise Comparison Method?

In the pairwise comparison method, Saatys consistency test is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons. Saaty suggested that the consistency ratio (CR) should be less than or equal to 0.1. Some researchers argued that the cut-off rule should be a function of the matrix size. In this paper, by simulation analysis, we find that, as the matrix size increases, the percent of the matrices with acceptable consistency (CR les 0.1) decreases dramatically, however, on the other hand, there will be more and more contradictory judgements in these sufficiently consistent matrices. This paradox shows that it is impossible to find some proper critical values of CR for different matrix sizes. Thus we argue that Saatys consistency test could be unreasonable.

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.

Fuzzy pricing of geometric Asian options and its algorithm

This paper considers the problem of pricing the geometric Asian option in the fuzzy environment. The fuzzy pattern of Kemma-Vorst formula is proposed under the assumption that the stock price, the risk-free interest rate and the volatility are all fuzzy numbers. An interpolation search algorithm is designed to solve the proposed pricing model. Furthermore, a numerical example is presented to show the rationality for the algorithm. Finally, an empirical study is also provided to indicate the practicability of the proposed fuzzy pricing model. From the empirical study, we can see that the market prices of E0015 option lay in the closed interval with belief degree 90% while the Kemma-Vorst model tends to underprice E0015 option. A general fuzzy pattern of geometric Asian option pricing is given.The specific fuzzy formulae of the Asian option pricing are obtained.The interpolation search algorithm is designed to solve the proposed pricing model. Owing to the fluctuations of the financial market, input data in the options pricing formula cannot be expected to be precise. This paper discusses the problem of pricing geometric Asian options under the fuzzy environment. We present the fuzzy price of the geometric Asian option under the assumption that the underlying stock price, the risk-free interest rate and the volatility are all fuzzy numbers. This assumption makes the financial investors to pick any geometric Asian option price with an acceptable belief degree. In order to obtain the belief degree, the interpolation search algorithm has been proposed. Some numerical examples are presented to illustrate the rationality and practicability of the model and the algorithm. Finally, an empirical study is performed based on the real data. The empirical study results indicate that the proposed fuzzy pricing model of geometric Asian option is a useful tool for modeling the imprecise problem in the real world.

Pricing black-scholes options with correlated credit risk and jump risk

This article follows the framework of Klein (1996) to present an improved method of pricing vulnerable options under jump diffusion assumptions about the underlying stock prices and firm values which are appropriate in many business situations. In contrast to Klein’s (1996) model, jumps allow not only for sudden changes in stock prices and firm values, but also for a firm to default instantaneously because of an unexpected drop in its value. Therefore, our model is able to provide sufficient conceptual insights about the economic mechanism of vulnerable option pricing. In particular, an analytical pricing formula for vulnerable European options under jump diffusion model is derived. The numerical results show that a jump occurrence in firm values can increase the likelihood of default and reduce the vulnerable option prices.

Pricing Currency Options in a Fuzzy Environment

Owing to the vague fluctuation of financial markets from time to time, the pricing parameters of currency option may occur imprecisely. In this case, it is natural to consider the fuzzy environment of exchange rate markets. In this paper, we introduce fuzzy techniques and obtain the fuzzy version of the Garman-Kohlhagen model. Assuming that the spot exchange rate, domestic interest rate, foreign interest rate, and the volatility are nonlinear fuzzy numbers, the fuzzy price of currency option is obtained. Then the financial analyst can choose any currency option with an acceptable belief degree for investorpsilas later decision making. At last, a numerical example based on the fuzzy version of the Garman-Kohlhagen model indicates that the fuzzy sets theory is a useful tool for modeling the imprecise problem in the real world.

A nonlinear program model to obtain consensus priority vector in the analytic hierarchy process

In group decision making, because the decision-makers usually represent different interest backgrounds, it is worth to study how to make the different decision makers coordinate and cooperate for aggregating group opinions. In this paper, based on the analytic hierarchy process, we propose a nonlinear program model to obtain consensus priority vector, and point that the model can make decision-makers reach consensus by improving compatibility of judgement matrices. Moreover, we use the genetic-simulated annealing algorithm to obtain its optimal solution. Finally, a numerical example is presented to illustrate the application of this method.