Financial Engineering

Demandable-debt finance by banks warrants explanation because it entails costs of bank suspension, liquidation, and idle reserve holdings. An explanation is developed in which demandable debt provides incentive-compatible intermediation where the banker has comparative advantage in allocating investment funds but may act against the interests of uninformed depositors. Demandable debt attracts funds by giving depositors an option to force liquidation. Its usefulness in transacting follows from information-sharing between monitors and nonmonitors.

In recent years, there has been a surge of research into methods for estimating derivatives of performance measures from sample paths of stochastic systems. In the case of queueing systems, typical performance measures are mean queue lengths, throughputs, etc., and the derivatives estimated are with respect to system parameters, such as parameters of service and interarrival time distributions. Derivative estimates potentially offer a general means of optimizing performance, and are useful in sensitivity analysis.

We establish strong consistency (i.e., almost sure convergence) of infinitesimal perturbation analysis (IPA) estimators of derivatives of steady-state means for a broad class of systems. Our results substantially extend previously available results on steady-state derivative estimation via IPA.

Let x(j) be the expected reward accumulated up to hitting an absorbing set in a Markov chain, starting from state j. Suppose the transition probabilities and the one-step reward function depend on a parameter, and denote by y(j) the derivative of x(j) with respect to that parameter. We estimate y(0) starting from the respective Poisson equations that x = [x(0),x(l), . . . ] and y = [y(0),y(l), . . . ] satisfy.

Generalized semi-Markov processes (GSMPs) and stochastic Petri nets (SPNs) are generally regarded as performance models (as opposed to logical models) of discrete event systems. Here we take the view that GSMPs and SPNS are essentially automata (generators) driven by input sequences that determine the timing of events. This view combines the deterministic, logical aspects and the stochastic, timed aspects of the two models.

In analyzing a stochastic system, such as a network of queues, one is often interested in how system performance depends on system parameters. Gradients provide useful information on this dependence. If the system in question is simulated (or perhaps just observed) one may therefore be interested in estimating gradients from sample paths.

This paper concerns production allocation in multicell manufacturing systems. The production objective is to track a nonstationary demand as closely as possible when the demand is near or exceeds the capacity of the system. The contribution of this paper is threefold. First, a series of approximations are proposed to obtain a model that is realistic while admitting a tractable solution. Second, we derive a general result on the second-order finite-time (transient) statistics of a continuous-time Markov chain.

In estimating functions of continuous-time Markov chains via simulation, one may reduce variance and computation by simulating only the embedded discrete-time chain. To estimate derivatives (with respect to transition probabilities) of functions of discrete-time Markov chains, we propose embedding them in continuous-time processes. To eliminate the additional variance and computation thereby introduced, we convert back to discrete time. For a restricted class of chains, we may embed in a continuous-time Markov chain and apply perturbation analysis estimation.

The issue of providing segment disclosures has renewed significance because the Securities & Exchange Commission (SEC) has been considering the extension of segment disclosures, both line-of-business (LOB) and geographically segmented (GEOG), to all interim financial statements. To determine whether GEOG data provide incremental information about the earnings process, the specific contribution of sales and income GEOG data was evaluated by estimating their predictive ability. Two sets of GEOG predictions were used in the predictive accuracy tests.