Duopolistic Competition and Capacity Choice with Jump-Diffusion Process


This paper studies the effects of sudden events on the optimal timing and capacity choice in a duopoly market. According to the characteristics of economic environment, we assume that the product demand follows geometric Brownian motion with a Poisson jump process. Under the settings, the firms face the risk of a sudden drop in demand which is caused by sudden events. We develop the real option game model to derive the investment equilibrium strategies. Moreover, the effects of sudden events on investment decisions are obtained by numerical analysis.

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Chen, D. (2015) Duopolistic Competition and Capacity Choice with Jump-Diffusion Process. Journal of Mathematical Finance, 5, 192-201. doi: 10.4236/jmf.2015.52018.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Smets, F. (1991) Exporting versus FDI: The Effect of Uncertainty, Irreversibilities and Strategic Interactions. Working Paper, Yale University, New Haven.
[2] Dixit, A. K. and Pindyck, R.S. (1994) Investment under Uncertainty. Princeton University Press, Princeton.
[3] Grenadier, S.R. (1996) The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets. The Journal of Finance, 51, 1653-1679.
[4] Weeds, H. (2002) Strategic Delay in a Real Options Model of R&D Competition. The Review of Economic Studies, 69, 729-747.
[5] Mason, R. and Weeds, H. (2010) Investment, Uncertainty and Pre-Emption. International Journal of Industrial Organization, 28, 278-287.
[6] Jorion, P. (1988) On Jump Processes in the Foreign Exchange and Stock Markets. Review of Financial Studies, 1, 427- 445.
[7] Bates, D.S. (1996) Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options. Review of Financial Studies, 9, 69-107.
[8] Merton, R.C. (1976) Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144.
[9] Kou, S.G. (2002) A Jump-Diffusion Model for Option Pricing. Management Science, 48, 1086-1101.
[10] Mason, C.F. and Wilmot, N.A. (2014) Jump Processes in Natural Gas Markets. Energy Economics, 46, S69-S79.
[11] Ko, C.-C., Lin, T.T. and Yang, C. (2011) The Venture Capital Entry Model on Game Options with Jump-Diffusion Process. International Journal of Production Economics, 134, 87-94.
[12] Pereira, P.J. and Armada, M.R. (2013) Investment Decisions under Hidden Competition. Economics Letters, 121, 228- 231.
[13] Pereira, P.J. and Rodrigues, A. (2014) Investment Decisions in Finite-Lived Monopolies. Journal of Economic Dyna- mics and Control, 46, 219-236.
[14] Besanko, D., Doraszelski, U., Lu, L.X. and Satterthwaite, M. (2010) Lumpy Capacity Investment and Disinvestment Dynamics. Operations Research, 58, 1178-1193.
[15] Jou, J.B. and Lee, T. (2008) Irreversible Investment, Financing, and Bankruptcy Decisions in an Oligopoly. Journal of Financial and Quantitative Analysis, 43, 769-786.
[16] Huisman, K. and Kort, P.M. (2013) Strategic Capacity Investment under Uncertainty. Tilburg University, Tilburg.
[17] Fudenberg, D. and Tirole, J. (1985) Preemption and Rent Equalization in the Adoption of New Technology. The Review of Economic Studies, 52, 383-401.

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