Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T03:35:06.608Z Has data issue: false hasContentIssue false

PREVENTION OF CATASTROPHIC FAILURES WITH WEAK FOREWARNING SIGNALS

Published online by Cambridge University Press:  19 November 2013

H. Dharma Kwon*
Affiliation:
Department of Business Administration, University of Illinois at Urbana-Champaign, Champaign, IL 61820. E-mail: [email protected].

Abstract

We consider the problem of a firm facing failures with weak forewarning signals. In the base model that we study, the firm watches for signals of a random arrival of a disruptive innovation and continuously updates the posterior probability that a disruptive innovation has already happened. A disruptive innovation is marked by a rapid increase in the growth rate of the market for a new technology, and it is followed by a random arrival of catastrophic failure of the firm. The firm can invest capital to adopt the innovation to prevent failure. The optimal policy is to adopt it when the posterior probability exceeds an optimally chosen threshold. We investigate the probability of failure under the optimal policy when the cost of failure is large and the arrival rate of disruptive innovation is low. The probability of failure is close to one if the arrival rate is extremely low while it is close to zero if the arrival rate is moderate. We also consider an extension of the base model to incorporate recurrence of disruptive innovation; when the arrival rate is moderate, the optimal threshold and the failure probability can be significantly larger than those of the base model.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Abramowitz, M. & Stegun, I.A. (1965). Handbook of mathematical functions. New York: Dover Publications.Google Scholar
2.Alvarez, L.H.R. (2001). Reward functionals, salvage values and optimal stopping. Mathematical Methods of Operations Research 54: 315337.CrossRefGoogle Scholar
3.Beibel, M. & Lerche, H.R. (1997). A new look at optimal stopping problems related to mathematical finance. Statistica Sinica 7: 93108.Google Scholar
4.Christensen, C.M. (2002). The innovator's dilemma. NY: Collins Business Essentials.Google Scholar
5.Christensen, C.M., Anthony, S.D. & Roth, E.A. (2004). Seeing what's next. Boston, MA: Harvard Business School Press.Google Scholar
6.Decamps, J.P., Mariotti, T. & Villeneuve, S. (2005). Investment timing under incomplete information. Mathematics of Operations Research 30(2) 472500.CrossRefGoogle Scholar
7.Economist (2005). Another Kodak moment (May 12).Google Scholar
8.Economist (2012). The last Kodak moment? (January 14).Google Scholar
9.Gapeev, P.V. (2010). Two switching multiple disorder problems for brownian motions. doi: arXiv:1011.0174.Google Scholar
10.Jensen, R. (1982). Adoption and diffusion of an innovation of uncertain profitability. Journal of Economic Theory 27(1) 182193.CrossRefGoogle Scholar
11.Kwon, H.D. & Lippman, S.A. (2011). Acquisition of project-specific assets with bayesian updating. Operations Research 59(5) 11191130.CrossRefGoogle Scholar
12.McCardle, K.F. (1985). Information acquisition and the adoption of new technology. Management Science 31(11) 13721389.CrossRefGoogle Scholar
13.Oksendal, B. (2003). Stochastic differential equations: an introduction with applications, 6th edn.Berlin, Germany: Springer.CrossRefGoogle Scholar
14.Peskir, G. & Shiryaev, A. (2006). Optimal stopping and free-boundary problems. Berlin, Germany: Birkhauser Verlag.Google Scholar
15.Poor, H.V. & Hadjiliadis, O. (2009). Quickest detection. Cambridge: Cambridge University Press.Google Scholar
16.Rapoport, A., Stein, W.E. & Burkheimer, G.J. (1979). Response models for detection of change. Boston: D. Reidel Publishing Company.CrossRefGoogle Scholar
17.Rosenberg, N. (1976). On technological expectations. Economic Journal 86(343) 523535.CrossRefGoogle Scholar
18.Ross, S.M. (1983). Introduction to stochastic dynamic programming. San Diego, CA: Academic Press.Google Scholar
19.Ryan, R. & Lippman, S.A. (2005). Optimal exit from a deteriorating project with noisy returns. Probability in the Engineering and Informational Sciences 19(03) 327343.CrossRefGoogle Scholar
20.Shiryaev, A. (1978). Optimal stopping rules. New York: Springer-Verlag.Google Scholar
21.Shiryaev, A.N. (1963). On optimum methods in quickest detection problems. Theory of Probability and its Applications 8 2246.CrossRefGoogle Scholar
22.Spector, M. & Mattioli, D. (2012). Kodak teeters on the brink. The Wall Street Journal. http://online.wsj.com/article/SB10001424052970203471004577140841495542810.html.Google Scholar
23.Ulu, C. & Smith, J.E. (2009). Uncertainty, information acquisition, and technology adoption. Operations Research 57(3) 740752.CrossRefGoogle Scholar