In many scheduling applications, minimizing delays is of high importance. One adverse effect of such delays is that the reward for completion of a job may decay over time. Indeed in healthcare settings, delays in access to care can result in worse outcomes, such as an increase in mortality risk. Motivated by managing hospital operations in disaster scenarios, as well as other applications in perishable inventory control and information services, we consider non-preemptive scheduling of jobs whose internal value decays over time. Because solving for the optimal scheduling policy is computationally intractable, we focus our attention on the performance of three intuitive heuristics: (1) a policy which maximizes the expected immediate reward, (2) a policy which maximizes the expected immediate reward rate, and (3) a policy which prioritizes jobs with imminent deadlines. We provide performance guarantees for all three policies and show that many of these performance bounds are tight. In addition, we provide numerical experiments and simulations to compare how the policies perform in a variety of scenarios. Our theoretical and numerical results allow us to establish rules-of-thumb for applying these heuristics in a variety of situations, including patient scheduling scenarios.

In this paper, some results on the complete moment convergence for arrays of rowwise negatively associated (NA, for short) random variables are established. The results obtained in this paper correct the corresponding one obtained in Ko [13] and also improve and generalize the corresponding ones of Kuczmaszewska [14] and Ko [13]. As an application of the main results, we present a result on complete consistency for the estimator in a non-parametric regression model based on NA errors. Finally, we provide a numerical simulation to verify the validity of our result.

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

In this paper, we present a new pricing model for vulnerable options, with time-varying variances for each asset described by Generalized Autoregressive Conditional Heteroscedasticity processes and correlated with the return of the asset. By connecting the underlying asset and the counterparty's assets through the market factor channel, the proposed model also captures stochastic correlation between the underlying asset return and the return of the counterparty's assets. The correlation depends on the levels of the variances of both assets and the market index as well. In the proposed framework, the closed-form solution for vulnerable options is derived and numerical results are presented to investigate the impact of counterparty default risk.

In this paper, we establish a fluid limit for a two-sided Markov order book model. The main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the “sell-side shape” and “buy-side shape” of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test the fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly traded stocks in certain time periods.

Temporal shaping of time series is the activity of deriving a time series model with a prescribed marginal distribution and some sample path characteristics. Starting with an empirical sample path, one often computes from it an empirical histogram (a step-function density) and empirical autocorrelation function. The corresponding cumulative distribution function is piecewise linear, and so is the inverse distribution function. The so-called inversion method uses the latter to generate the corresponding distribution from a uniform random variable on [0,1), histograms being a special case. This paper shows how to manipulate the inverse histogram and an underlying marginally uniform process, so as to “shape” the model sample paths in an attempt to match the qualitative nature of the empirical sample paths, while maintaining a guaranteed match of the empirical marginal distribution. It proposes a new approach to temporal shaping of time series and identifies a number of operations on a piecewise-linear inverse histogram function, which leave the marginal distribution invariant. For cyclical processes with a prescribed marginal distribution and a prescribed cycle profile, one can also use these transformations to generate sample paths which “conform” to the profile. This approach also improves the ability to approximate the empirical autocorrelation function.

Under some mild conditions, the strong consistency and complete consistency of the LS estimators in the errors-in-variable regression model with weakly negative dependent errors are obtained, which generalize the corresponding ones for negatively associated random variables. In addition, the simulation study shows that the biases of our method are small, and our method performs well.