The stochastic sequential assignment problem (SSAP) allocates distinct workers to sequentially arriving tasks with stochastic parameters to maximize the expected total reward. In this paper, the assignment of tasks is performed under the threshold criterion, which seeks a policy that minimizes the probability of the total reward failing to achieve a target value. A Markov-decision-process approach is employed to model the problem, and sufficient conditions for the existence of a deterministic Markov optimal policy are derived, along with fundamental properties of the optimal value function. An algorithm to approximate the optimal value function is presented, and convergence results are established.

We introduce a natural growth model for directed series-parallel (SP) graphs and look at some of the graph properties under this stochastic model. Specifically, we look at the degrees of certain types of nodes in the random SP graph. We examine the degree of a pole and will find its exact distribution, given by a probability formula with alternating signs. We also prove that, for a fixed value s, the number of nodes of outdegree 1, …, s asymptotically has a joint multivariate normal distribution. Pólya urns will systematically provide a working tool.

We examine the time-dependent behavior of a birth–death process, whose birth rates and death rates are decreasing and increasing, respectively, with respect to the current state. Such models can be used to describe Markovian queueing systems with exponential reneging, where potential arrivals balk with a certain probability that depends on the number of customers observed upon arrival. Our results are derived by interpreting the birth–death process as the queue-length process of what we refer to as the “knockout queue.”

Expansions for moments of $\overline{X}$, the mean of a random sample of size n, are given for both the univariate and multivariate cases. The coefficients of these expansions are simply Bell polynomials. An application is given for the compound Poisson variable SN, where $S_{n} = n \overline{X}$ and N is a Poisson random variable independent of X1, X2, …, yielding expansions that are computationally more efficient than the Panjer recursion formula and Grubbström and Tang's formula.

In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single- and multi-server settings. In all models, we obtain the Laplace transform of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures.

The P–P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P–P order based on P–P plots. For a pair of random variables (X1, Y1) and (X2, Y2) one can see the relative precedence of Y2 over X2 versus that of Y1 over X1 using P–P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the help of this new partial order. Several concepts of positive dependence can also be expressed in terms of P–P orders of the conditional distributions.

This note introduces bivariate dual generalized Marshall–Olkin distribution and builds a comparison result on the copula of this distribution. Several applications in survival analysis and actuarial science are presented as well.

Motivated by the fact that many investors have limited ability to update the expectation regarding future stock returns with the arrival of new information instantly, this paper provides a continuous-time model to study the performance of passive trading strategies. We derive the true Sharp ratio of the passive strategies in terms of the mean and variance of an explicit stochastic process. Based on this expression, we quantify the impact of partial information by performing a thorough comparative static analysis. Such an analysis provides a rationale for why investors with inaccurate information about stock return behave better in the mean-reverting environment than in the i.i.d. environment and why pessimistic investors can achieve better performance than optimistic ones. As a by-product, we propose an analytical approach to compute the “implied” parameters in stock return predictor for both i.i.d. and mean-reverting dynamics, which seems interesting for future research.