Irreversible investment problems
This paper focuses on the problem of investing in an uncertain market, when the investments are considered to be irreversible. This means that once an investment has been made and the market later drops to a less favorable state, one cannot undo the investment. The risk of overinvesting means that we should wait longer to invest, than if the investments were totally or partially reversible. On the other hand one does not want to wait too long and miss out on any profits due to our lack of capacity. The problem then is to find a proper investment strategy taking the fluctuating marked into account. Numerous examples of irreversible investments exist, for example purchase of highly specified production machinery, educating staff members or spending money on advertising. It is assumed that the investments have two effects on given economy. The first is that the income will increase. The other effect of an investment is obviously that it costs money. It is also assumed that an investment has different costs depending on what the capacity is and naturally also depending on how much one wants to increase the capacity. The author gives some implicit conditions for a solution in the case where the market process is \(n\)-dimensional and an explicit solution in the one-dimensional case. This paper uses the theory developed by \textit{E. B. Dynkin} [``Markov processes''. Vol. I, II (1965; Zbl 0132.37701)]\ to solve the problem. The paper also provides some generalization to find the specific solution to the irreversible investment problem.
scientific article; zbMATH DE number 1524268