The Martingale Evolution of Price Forecasts in a Supply Chain Market for Capacity : Technical Report

We develop a continuous time analog of the Martingale Model of Forecast Evolution (MMFE) and show that the discrete time MMFE is a special case of our model. We apply the continuous time MMFE to model the forecast evolution of the instantaneous rate of demand in a market for capacity. Using the Stochastic Maximum Principle, we show that the equilibrium market price and the optimal market production rate evolve as martingales. Finally, we study the relationship between the resolution of the demand uncertainty and the resolution of the market price uncertainty. We find that the rate of resolving price uncertainty increases as the rate of resolving demand uncertainty increases. Also, we find that the resolution of price uncertainty occurs more uniformly over time if the cost of overtime/undertime increases. ∗School of Operations Research and Industrial Engineering, Cornell University, 278 Rhodes Hall, Ithaca, NY 14853, USA. Tel: (607) 255-8153. Email: as236@cornell.edu. †School of Operations Research and Industrial Engineering, Cornell University, 218 Rhodes Hall, Ithaca, NY 14853, USA. Tel: (607) 255-9122. Email: pj16@cornell.edu.

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