A Mean-Variance Approach to Capital Investment Optimization
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We develop an improved model of capital investment under uncertainty that incorporates the variance of the capital stock in the payoff functional to manage risk. Our model results in a mean field type control problem that cannot be solved by classical stochastic control methods. We solve our problem using techniques presented in Bensoussan, Frehse, and Yam [Mean Field Games and Mean Field Type Control Theory, Springer, New York, 2013]. The explicit solution is a feedback depending on the initial condition. Moreover, our model can be reduced to Abel's [Amer. Econ. Rev., 73 (1983), pp. 228-233]. Numerical results suggest that the risk reduction optimally exceeds the cost incurred. Following Björk, Khapko, and Murgoci [Finance Stoch., 21 (2017), pp. 331-360], we solve for a time-consistent solution, i.e., the best possible feedback independent of the initial condition. The time-consistent policy discards our risk specification, with the resultant loss of value to the firm. © 2019 Society for Industrial and Applied Mathematics
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