Irreversible capital accumulation with economic impact
The authors consider an irreversible capacity expansion model which is a special case of a more general model [\textit{T. Ø. Kobila}, Stochastics Stochastics Rep. 43, No. 1--2, 29--63 (1993; Zbl 0825.93981)]. Market uncertainty is modeled by a geometric Brownian motion and additional investment is assumed to have a strictly negative effect on an underlying economic indicator process. The authors formulate an optimization problem which becomes a singular stochastic control problem [\textit{V. E. Benes} et al., Stochastics 4, 39--83 (1980; Zbl 0451.93068)] and an explicite solution is found using the Hamilton-Jacobi-Bellman machinery. The changes in the state process caused by optimal control action are proportional to the state process itself. Although interesting from stochastic control theory perspective the results seem to be too complicated from the economy point of view.
scientific article; zbMATH DE number 6759150
scientific article