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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2002-42
December 2002

A discrete time model of investment under non-Gaussian shocks


Svetlana Boyarchenko, Sergei Levendorskii


A discrete time model of irreversible investment is explored. The investor is a risk-neutral, value maximizing competitive firm. The unit price of the firm's output follows a non-Gaussian stochastic process. Under weak restrictions on the process and the firm's production function, explicit formulas for the optimal trigger price of investment and the value of the firm are derived. Advantages of discrete time setting are exploit to reduce the computation to a relatively simple procedure. A new method of solving optimization problems under uncertainty based on the Wiener-Hopf factorization in the form natural for Economics is suggested.

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