A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

Hymer and Uneven Development Revisited: Foreign Direct Investment and Regional Inequalities

Picking up on one of Hymer's key contributions, this paper examinesthe impact that inward foreign direct investment (FDI) intothe UK has on the patterns of development, both within and acrossregions. Using a panel of data for the manufacturing sector,the paper illustrates that even where one isolates the effecton the domestic sector alone, inward investment acts to increasethe demand for skilled, relative to unskilled labour, and alsogenerates the expected agglomeration effects in terms of thedemand for capital investment. The paper then goes on to drawcertain policy comparisons between these findings and the desiredaim of attracting FDI, notably to increase demand for labourin those regions suffering structural unemployment, and secondlyto reduce the disparities between regions.     

Leveling the playing field: factors influencing trade show success for small companies

Recent research indicates that trade shows are a place to find prospects and close sales. Yet, many requisites of success found in prior studies may not be available to companies with limited resources. A study that compares the activities of successful vs. unsuccessful exhibitors from small companies was conducted. Results indicate similar budgets, yet very different results. Factors influencing success include strategic factors such as centering responsibility in one position, as well as tactical decisions such as those regarding pre-show promotion.     

Reconfiguring supplier relationships between local and global: History matters

Small and medium-sized companies are increasingly facing international markets as part of their processes of growth and development. A great deal of literature deals with different patterns of growth and international development that are specific to SMEs with respect to large companies. Fewer studies have been conducted on the reconfiguration of company supplier relationships involved in these processes. This paper focuses on the role played by the consolidated set of company supplier relationships when the firm faces some critical stages in its process of development, i.e., growth from small to mid-sized and the implementation of new ventures abroad accessing new business relationships with international suppliers. A multiple and longitudinal case study shows how the local set of supplier relationships of four mid-sized Italian mechanical companies acting in industrial districts has played an important role in shaping the emerging set of supplier relationships and addressing companies' actions in their growth and internationalization processes.     

The impact of coercive and non-coercive forms of influence on trust, commitment, and compliance in supply chains

A major premise in managing channel relationships is encouraging cooperation to achieve the aims of the relational partners. This often requires a balancing act between utilization of influence across the supply chain to motivate decisions, while employing tactics that do not damage the future of the relationship. This paper builds and tests a model of how influence strategies affect relational elements, specifically trust and commitment, which both promote strong inter-firm relationships and act as mediators of joint action, specifically cooperation and compliance across channel partners. Results suggest that coercive strategies are counterproductive in encouraging cooperation and compliance either directly or through relational intermediaries, while non-coercive influence produces positive outcomes and effects on intermediaries. Low levels of coercive influence do appear to generate positive outcomes. Managerial implications and future research based on these results conclude the paper.     

Comparing two territory partitions in districting problems: Indices and practical issues

Planning as part of public sector decision-making situations is an activity of critical importance, with direct relevance for urban planners. The ramifications of such decisions generally have significant effect on peoples’ lives. The current paper deals with the comparison between territorial maps in the context of districting problems with a strong socio-economic component. The theoretical problem involves the comparison of two partitions in a connected, undirected, and planar graph. In considering this problem, we introduce three new indices to compare territory partitions: compatibility, inclusion, and distance, all of which have importance for real-world planning situations. Numerical experiments of these indices were carried out for the communes network in (Iˆle de France), France.