Financial Engineering

Infinitesimal perturbation analysis is a method of obtaining estimates of performance sensitivity through simulation of a stochastic system. Expressions are derived for the limiting value of a broad class of such estimators associated with queueing networks, in terms of the unique solution to a set of linear equations. The approach used is to augment the underlying queueing process with information about which servers have been "perturbed" and by how much.

Two methods are presented for estimating performance derivatives from simulation of multi-class queueing networks for sensitivity analysis. The methods use approximate subnetwork aggregation to reduce the problem to a single-class derivative estimation problem with which a modified infinitesimal perturbation analysis algorithm is used. The modified algorithm treats a subnetwork as though it had been aggregated, but is actually applied to the original (non-aggregated) network.

In this article we construct a model in which a consumer's utility depends on the consumption history. We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closed form in this general equilibrium setting to rationalize the observed stickiness of the consumption series relative to the fluctuations in stock market wealth. The sample paths of consumption generated from this model imply lower variability in consumption growth rates compared to those generated by models with separable utility functions.

A bilateral moral-hazard problem provides a rationale for "up-or-out" employment contracts. The employer sets a wage higher than opportunity cost to induce the worker to invest in firm-specific capital. If the individual does not make the grade, it is in the firm's interest ex post to fire him. Had the initial arrangement not included provisions for firing individuals, the firm would underreport the value of the employee, wrecking the incentive scheme. The basic model permits both firm and worker to be risk neutral.

This paper presents a strategic theory of contract renegotiation. In this theory, suboptimal contracts are put in place initially to protect one party against undesirable actions by another party and are renegotiated once the danger is past. We develop a model to establish the cases in which simple contracts cannot achieve desirable outcomes, so that only a complicated contract or renegotiation will serve. Unlike most previous accounts of contract renegotiation, this theory does not rely on exogenous uncertainty to motive renegotiation.

Using a birth and death process as an illustrative example, we introduce the notion of alternative representations of stochastic processes and discuss its importance for infinitesimal perturbation analysis derivative estimation. Through a different choice of representation, we are led to an IPA algorithm for a birth and death process better than one discussed by other authors.

Often the timing of certain activities has a strong periodic element. Due to circumstances an activity is sometimes made outside the regular cycle, but it does not break the cycle. Thus, the timing of future activities is highly predictable. We provide a stochastic model where the data are not seasonal yet the optimal behaviour has a strong periodic element.

This paper studies the relation between Value Line's successful record in predicting relative stock price movements and the firm size effect. The data suggest little direct relation between the two phenomena. Value Line tends not to rank small firm stocks, and small firm stocks that are ranked are more likely to receive a low rank than large firm stocks. Within each size-sorted quintile of the market, the mean payoffs on costless positions constructed according to Value Line's recommendations are positive.