John M. Cozzolino

A Service System with Unfilled Requests Repeated

The object of this paper is to analyze a model of a queuing system in which customers cannot be in continuous contact with the server, but must call in to request service: If the server is free, then the next request to arrive is served immediately; if the server is occupied, however, the unsatisfied customer must break contact and later re-initiate his request. Thus, repeat requests for service from the pool of unsatisfied customers are superimposed on the normal stream of arrivals of first attempts. This system is characteristic of situations in which there is a single operator or source of information that must be called and busy signals are not held. This paper calculates several characteristic quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first requests and repeat requests.

The Maximum-Entropy Distribution of the Future Market Price of a Stock

This paper uses the principle of maximum entropy to construct a probability distribution of future stock price for a hypothetical investor having specified expectations. The result obtained is in good agreement with observations recorded in the literature. Thus, the paper concludes that the hypothetical individual investor is representative of a large class of investors. This new derivation of the well known random-walk theory of stock-price movements leads to an improved understanding of the model parameters by relating the variance of the random-walk process to the risk aversion of the investors. A practical use of the model is proposed to help the investor form an objective opinion of his skill.

Sequential Search for an Unknown Number of Objects of Nonuniform Size

This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area. All target objects are initially present in the search area and remain at least until discovered; no new objects are generated during the search process. Targets are not moveable. The search process is characterized by the quantity of search effort. The model describes the distribution of the number and sizes of target objects present. The probability of discovery is assumed proportional to object size. The paper gives many results, including the probability distribution of the number and sizes of discovered objects, and the prior and posterior distributions of the number of objects remaining undiscovered. Then it gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process.

Conjugate Distributions for Incomplete Observations

Abstract Reliability data often include information that the failure event has not yet occurred for some items, while observations of complete lifetimes are available for other items. Bayesian analysis requires a conjugate posterior density function after any combination of complete and incomplete observations. This paper considers density functions having failure rate function consisting of a known function multiplied by an unknown scale factor. It is shown that a gamma family of priors is conjugate for both complete and incomplete experiments. A very flexible and convenient model results from the assumption of a piecewise constant failure rate function.

The analysis of risky portfolios by geometric programming

SummaryThe problem of selecting a portfolio from a set of risky business ventures is considered. It is formulated as a maximization of the risk-adjusted (certainty-equivalent) profit for the portfolio based upon the exponential utility function and analysed via generalised geometric programming. Generalised geometric programming provides dual programs for the general case and for particular probability distributions. The particular cases of gamma, binomial, and normal distributions are converted into duals which arc of one dimension regardless of the number of portfolios.ZusammenfassungAusgangspunkt dieses Aufsatzes ist das folgende Portfolio-Problem: Ein gegebenes Budget ist auf verschiedene Anlagemöglichkeiten so aufzuteilen, daß dabei der erwartete Nutzen des Gesamtertrages maximiert wird. Dieses Problem wird — zunächst ohne Verwendung einer Wahrscheinlichkeitsverteilung für die Erträge der einzelnen Anlagemöglichkeiten — mit Hilfe der verallgemeinerten geometrischen Programmierung analysiert. Es werden duale Programme abgeleitet, die die Lösung des Portfolio-Problems für verschiedene spezielle Verteilungsfunktionen in sehr einfacher Weise gestatten.