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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

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Modelling the number of customers as a birth and death process

Pinto, H. and Howell, S. and Paxson, D. (2009) Modelling the number of customers as a birth and death process. European Journal of Finance, 15 (2). pp. 105-118. ISSN 1351-847X

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Abstract

Birth and death may be a better model than Brownian motion for many physical processes, which real options models will increasingly need to deal with. In this paper, we value a perpetual American call option, which gives the monopoly right to invest in a market in which the number of active customers (and hence the sales rate) follows a birth and death process. The problem contains a singular point, and we develop a mixed analytic/numeric method for handling this singular point, based on the method of Frobenius. The method may be useful for other cases of singular points. The birth and death model gives lower option values than the geometric Brownian motion model, except at very low volatilities, so that if a firm incorrectly assumes a geometric Brownian motion process in place of a birth and death process, it will invest too seldom and too late.