## Explicit solution of a consumption/investment problem.(English)Zbl 0622.90018

Stochastic optimization, Proc. Int. Conf., Kiev/USSR 1984, Lect. Notes Control Inf. Sci. 81, 59-69 (1986).
[For the entire collection see Zbl 0585.00014.]
Authors’ summary: ”This paper solves an optimal stochastic control problem which arises in finance. Specifically, we characterize the optimal consumption and investment policies of an individual who allocates his wealth into two investments, one which is deterministic with rate of increase r, while the other is given by a log Brownian motion process with rate of increase $$\alpha\neq r$$ and variance $$\sigma^ 2$$. The individual seeks to maximize $E_ x(\int^{\infty}_{0}e^{-\beta t}U(c_ t)dt),$ where $$c_ t\geq 0$$ represents the consumption rate, $$\beta$$ is a discount factor, and U is a utility function. We assume $$\pi_ t$$ represents an investment control and denotes the fraction of wealth allocated to the log Brownian motion investment.”
Reviewer: K.Wickwire

### MSC:

 91B62 Economic growth models 93E20 Optimal stochastic control

Zbl 0585.00014