Snapshot samples

We consider a coverage model where an initial event that occurs at some point in time triggers an activity of random duration that leads to some subsequent event. A snapshot sample is constructed at a fixed point in chronological time either by sampling only subjects where the initial event has occurred but the subsequent event has yet to occur (active subjects), or by sampling only subjects where both the initial and subsequent events have occurred (inactive subjects). The biases inherent in snapshot sampling can be neatly characterized by the properties of two random variables: the history (defined as the time the initial event occurs as measured into the past from the chronological point of sampling), and the active time (defined as the length of time between the initial and subsequent events). Though snapshot samples are biased, recognizing the biases enables correct inferences to be drawn from snapshot-sampled data. Considering only the case where and are independent random variables, this paper presents the probability models associated with snapshot sampling, demonstrates the problems that can occur, offers procedures for overcoming these problems, and applies the methods to interesting data sets.     

From edgeworth to fisher to vickrey: A comment on Michael J. Boskin's Vickrey lecture

Irving Fisher has been overlooked as an influence on William Vickrey's work on taxation and as a link between Edgeworth and Vickrey. Vickrey was Fisher's last and greatest student.     

E-banking comes to town: Exploring how traditional UK high street banks are meeting the challenge of technology and virtual relationships

UK high street banks are continuing to extend the choice of channel through which customers can manage their moneycolon; an obvious example is e-banking. They have been keen to exploit technological advances and changing customer attitudes to alternative channels. Additionally, competition from leaner new market entrants has provided an added incentive to adopt new approaches. In the light of such developments, it is worth reflecting on the changing nature of the bank–customer relationship. This paper suggests that banks are finding it difficult to manage relationships effectively due, in large measure, to the sheer volume of customer data generated by new interactive, technology-based channels. Paradoxically, it seems that the more data banks have about customers the less likely they are to know them on a personal level. It is further suggested that channels such as e-banking potentially reduce the level of personal contact between bank and customer to the extent that a ‘virtual’ relationship develops. This paper concludes that, given the tendency towards ‘virtualisation’, it is inconceivable that bank–customer relationships will become any more intimate in the future. Indeed, a greater degree of personalisation in customer communication may be the very best that banks are able to offer.     

A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.     

Analysis of Beef Producers' Risk Management Perceptions and Desire for Further Risk Management Education

Beef cattle producers were surveyed in Texas and Nebraska to investigate perceptions of sources of risk, the effectiveness of risk management strategies, and interest in further risk management education, particularly production risk, using probit analysis. Important decision variables identified are age, prior use of risk management tools, previous attendances of risk management education, and risk aversion. Severe drought and cattle price variability are identified as primary risk factors with potential to affect farm income. Extremely cold weather and disease are of less importance. Understocking pasture and storing hay are perceived most effective as risk management options.