Applied Stochastic Models in Business and Industry

Nkurunziza, Sévérien; Ahmed, S. Ejaz

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.775

We consider some inference problems concerning the drift parameters of multi‐factors Vasicek model (or multivariate Ornstein–Uhlebeck process). For example, in modeling for interest rates, the Vasicek model asserts that the term structure of interest rate is not just a single process, but rather a superposition of several analogous processes. This motivates us to develop an improved estimation theory for the drift parameters when homogeneity of several parameters may hold. However, the information regarding the equality of these parameters may be imprecise. In this context, we consider Stein‐rule (or shrinkage) estimators that allow us to improve on the performance of the classical maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, their relative dominance is explored and assessed. We illustrate the suggested methods by analyzing interbank interest rates of three European countries. Further, a simulation study illustrates the behavior of the suggested method for observation periods of small and moderate lengths of time. Our analytical and simulation results demonstrate that shrinkage estimators (SEs) provide excellent estimation accuracy and outperform the MLE uniformly. An over‐ridding theme of this paper is that the SEs provide powerful extensions of their classical counterparts. Copyright © 2009 John Wiley & Sons, Ltd.

Chen, Ping; Yang, Hailiang

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.776

This paper extends the pension funding model in (N. Am. Actuarial J. 2003; 7:37–51) to a regime‐switching case. The market mode is modeled by a continuous‐time stationary Markov chain. The asset value process and liability value process are modeled by Markov‐modulated geometric Brownian motions. We consider a pension funding plan in which the asset value is to be within a band that is proportional to the liability value. The pension plan sponsor is asked to provide sufficient funds to guarantee the asset value stays above the lower barrier of the band. The amount by which the asset value exceeds the upper barrier will be paid back to the sponsor. By applying differential equation approach, this paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In addition, we study the effects of different barriers and regime switching on the results using some numerical examples. The optimal dividend problem is studied in our examples as an application of our theory. Copyright © 2009 John Wiley & Sons, Ltd.

Chen, Ping; Wang, Jinde

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.780

In regression model with stochastic design, the observations have been primarily treated as a simple random sample from a bivariate distribution. It is of enormous practical significance to generalize the situation to stochastic processes. In this paper, estimation and hypothesis testing problems in stochastic volatility model are considered, when the volatility depends on a nonlinear function of the state variable of other stochastic process, but the correlation coefficient |ρ|≠±1. The methods are applied to estimate the volatility of stock returns from Shanghai stock exchange. Copyright © 2009 John Wiley & Sons, Ltd.

He, Zhen; Wang, Jing; Oh, Jinho; Park, Sung H.

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.788

Typically in the analysis of industrial data for product/process optimization, there are many response variables that are under investigation at the same time. Robustness is also an important concept in industrial optimization. Here, robustness means that the responses are not sensitive to the small changes of the input variables. However, most of the recent work in industrial optimization has not dealt with robustness, and most practitioners follow up optimization calculations without consideration for robustness. This paper presents a strategy for dealing with robustness and optimization simultaneously for multiple responses. In this paper, we propose a robustness desirability function distinguished from the optimization desirability function and also propose an overall desirability function approach, which makes balance between robustness and optimization for multiple response problems. Simplex search method is used to search for the most robust optimal point in the feasible operating region. Finally, the proposed strategy is illustrated with an example from the literature. Copyright © 2009 John Wiley & Sons, Ltd.

Abanto‐Valle, Carlos A.; Migon, Helio S.; Lopes, Hedibert F.

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.789

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.

Grömping, Ulrike; Landau, Sabine

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.773

Shapley value regression consists of assessing relative importance and accordingly adjusting regression coefficients. It is argued that adjustment of coefficients is unnecessary and even misleading for practically relevant situations. Examples are given, and an alternative procedure is proposed for situations for which the coefficients are requested to have a certain sign. Copyright © 2009 John Wiley & Sons, Ltd.

Lipovetsky, Stan; Conklin, W. Michael

2010 Applied Stochastic Models in Business and Industry

doi: 10.1002/asmb.829