We consider asset allocation strategies for the case where an investor can allocate his wealth dynamically between a risky stock, whose price evolves according to a geometric Brownian motion, and a risky bond, whose price is subject to negative jumps due to its credit risk and therefore has discontinuous sample paths. We derive optimal policies for a number of objectives related to growth. In particular, we obtain the policy that minimizes the expected time to reach a given target value of wealth in an exact explicit form. We also show that this policy is exactly equivalent to the policy that is optimal for maximizing logarithmic utility of wealth and, hence, the expected average rate at which wealth grows, as well as to the policy that maximizes the actual asymptotic rate at which wealth grows. Our results generalize and unify results obtained previously for cases where the bond was risk-free in both continuous- and discrete-time.

In this paper we consider the use of coupling ideas in efficiently computing a certain class of transient performance measures. Specifically, we consider the setting in which the stationary distribution is unknown, and for which no exact means of generating stationary versions of the process is known. In this context, we can approximate the stationary distribution from empirical data obtained from a first-stage steady-state simulation. This empirical approximation is then used in place of the stationary distribution in implementing our coupling-based estimator. In addition to the empirically based coupling estimator itself, we also develop an associated confidence interval procedure.

The length biased distribution occurs naturally for some sampling plans in reliability, biometry, and survival analysis. In this note, inequalities for length biased distributions are proved for monotone hazard functions and mean residual life functions. The problem of sampling and selection of experiments from the length biased distribution as opposed to the original distribution is addressed. Certain modified cross-entropy measures are also investigated.

We study the Birnbaum importance of the consecutive-k-out-of-n line and clear up confusion in some claimed but unproved results. We introduce some new techniques which not only prove these claimed results but also generalize them much further. Finally, we extend our results to the 2-out-of-m-out-of-n line.

In this paper, we give characterizations of nonparametric families of life distributions based on aging and variability orderings of the residual life of k-out-of-n systems. We obtain some results of increasing (decreasing) failure rate classes as well as of new classes decreasing (increasing) mean residual life of the system and new better (worse) than used in expectations of the system. Relationships among themselves and others such as new better (worse) than used, new better (worse) than used expectations, and decreasing (increasing) mean residual life are also given.

We obtain necessary and sufficient moment conditions for exponentiality among all class ℒ aging distributions. This result, which solves an open problem, is derived as a consequence of the answer to a more general question of investigating conditions for stochastic equivalence of Laplace ordered nonnegative r.v.'s and its ramifications.

We are interested in E [N], the mean time until the most recent k values of a sequence of independent and identically distributed random variables exceeds a specified constant. Using recent results, we present a simulation procedure for determining E [N]. These results are also used to obtain upper and lower bounds for E [N]. These bounds, however, are in terms of a quantity ω that is not easily calculated. A recursive procedure for evaluating ω when the data distribution is Bernoulli is given. Efficient simulation procedures for estimating ω in the cases of normal and exponential population distributions are also presented, as is a Markov chain monte carlo procedure when the distribution is general.

In this paper, we provide counterexamples to a conjecture, made by Miyazawa and Tijms (1993), on the upper and lower bounds for the loss probability in finite-buffer queues.

This note presents an example indicating for denumerable Markov decision chains that nonexistence of the Laurent expansion of the α-discounted rewards in α = 1 implies also nonexistence of the Puiseux expansion.

We consider the problem of estimation of the standard deviation σ and the process capability indices Cp and Cpm for a normally distributed process. The problem is addressed with the objective of obtaining optimal estimators under the classic criterion of minimum variance unbiased estimation, as well as under the Pitman measure of closeness.