Model-free portfolio theory: A rough path approach

Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Föllmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case of functionally generated portfolios to a pathwise version of the so-called master formula of classical SPT. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Cover's universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by showing that (nonfunctionally generated) log-optimal portfolios in an ergodic Itô diffusion setting have the same asymptotic growth rate as Cover's universal portfolio and the best retrospectively chosen one.     

Clustering and compatibility between tourism attractions

Cumulative attraction or compatibility is a powerful factor in locational decisions of retail outlets, but it has received little attention in the tourism literature. Existing studies largely ignore the impact of spatial and thematic clustering on compatibility between tourism businesses. This research questions whether and how spatial and thematic clustering are related to tourist movements between visitor attractions. The study in Cornwall, England, is based on in‐depth interviews with tourist attraction managers and key informants, complemented by a survey of 435 tourists. It provides insights into the relationship between the nature of the tourism product, spatial clustering and tourism behaviour. Copyright © 2009 John Wiley & Sons, Ltd.