Minimax price bounds in incomplete markets

This paper develops an approach to tighten the bounds on asset prices in an incomplete market by combining no-arbitrage pricing and preference-based pricing, and the approach is applied to a call option in the absence of dynamic rebalancing. With the no-arbitrage pricing, it is straightforward to obtain the initial bounds, which are too wide to be of practical uses. By accepting that a representative agent exhibits risk aversion from a benchmark pricing kernel, it is possible to narrow the bounds considerably. Using the unbiased minimax deviation implicit in the parameters, one can restrict further the set of reasonable values on assets in incomplete markets.     

Dispersive ordering of fail-safe systems with heterogeneous exponential components

Let X ₁, . . . , X _n be independent exponential random variables with respective hazard rates λ₁, . . . , λ _n , and Y ₁, . . . , Y _n be independent and identically distributed random variables from an exponential distribution with hazard rate λ. Then, we prove that X _2:n , the second order statistic from X ₁, . . . , X _n , is larger than Y _2:n , the second order statistic from Y ₁, . . . , Y _n , in terms of the dispersive order if and only if

$\lambda\geq \sqrt{\frac{1}{{n\choose 2}}\sum_{1\leq i < j\leq n}\lambda_i\lambda_j}.$

We also show that X _2:n is smaller than Y _2:n in terms of the dispersive order if and only if

$ \lambda\le\frac{\sum^{n}_{i=1} \lambda_i-{\rm max}_{1\leq i\leq n} \lambda_i}{n-1}. $

Moreover, we extend the above two results to the proportional hazard rates model. These two results established here form nice extensions of the corresponding results on hazard rate, likelihood ratio, and MRL orderings established recently by Pǎltǎnea (J Stat Plan Inference 138:1993–1997, 2008), Zhao et al. (J Multivar Anal 100:952–962, 2009), and Zhao and Balakrishnan (J Stat Plan Inference 139:3027–3037, 2009), respectively.

     

Distribution of run statistics in partially exchangeable processes

Let { X_i} _{i 3 1}{{ X_{i}} _{igeq 1}} be an infinite sequence of recurrent partially exchangeable binary random variables. We study the exact distributions of two run statistics (total number of success runs and the longest success run) in { X_i} _{i 3 1}{{ X_{i}} _{igeq1}} . Since a flexible class of models for binary sequences can be obtained using the concept of partial exchangeability, as a special case of our results one can obtain the distribution of runs in ordinary Markov chains, exchangeable and independent sequences. The results also enable us to study the distribution of runs in particular urn models.     

Noncentral bimatrix variate generalised beta distributions

In this paper, we determine the density functions of nonsymmetrised doubly noncentral matrix variate beta type I and II distributions. The nonsymmetrised density functions of doubly noncentral and noncentral bimatrix variate generalised beta type I and II distributions are also obtained.     

Exact inference for progressively Type-I censored exponential failure data

For reasons of time constraint and cost reduction, censoring is commonly employed in practice, especially in reliability engineering. Among various censoring schemes, progressive Type-I right censoring provides not only the practical advantage of known termination time but also greater flexibility to the experimenter in the design stage by allowing for the removal of test units at non-terminal time points. In this article, we consider a progressively Type-I censored life-test under the assumption that the lifetime of each test unit is exponentially distributed. For small to moderate sample sizes, a practical modification is proposed to the censoring scheme in order to guarantee a feasible life-test under progressive Type-I censoring. Under this setup, we obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and derive the exact sampling distribution of the MLE under the condition that its existence is ensured. Using the exact distribution of the MLE as well as its asymptotic distribution and the parametric bootstrap method, we then discuss the construction of confidence intervals for the mean parameter and their performance is assessed through Monte Carlo simulations. Finally, an example is presented in order to illustrate all the methods of inference discussed here.     

Performance trends in the construction industry worldwide: an overview of the turn of the century

This paper presents an exploratory study to assess the efficiency level of construction companies worldwide, exploring in particular the effect of location and activity in the efficiency levels. This paper also provides insights concerning the convergence in efficiency across regions. The companies are divided in three regions (Europe, Asia and North America), and in the three main construction activities (Buildings, Heavy Civil and Specialty Trade). We analyze a sample of 118 companies worldwide between 1995 and 2003. Data envelopment analysis is used to estimate efficiency, and the Malmquist index is applied for the evaluation of productivity change. Both methods were complemented by bootstrapping to refine the estimates obtained. A panel data truncated regression with categorical regressors is used to explore the impact of location and activity in the efficiency levels. The results reveal that the efficiency of North American companies is higher than the European and Asian counterparts. Other important conclusion points to a convergence in efficiency levels across regions as in North America productivity remains stable, whereas in Asia and Europe productivity improves.