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**Optimal consumption and portfolio policies with an infinite horizon: Existence and convergence.**
*(English)*
Zbl 0749.60039

In the last time many papers address the optimal consumption and portfolio problem in economies with a finite horizon. In the present work the authors show how the set of new tools can be brought to bear on the same problem in economies with an infinite horizon. They come to the conclusion that, excepting for some important technical departures, the existence and computation of an optimal policy can be analyzed similarly with the same attractive features as in finite horizon economies. The convergence of optimal policies in finite horizon economies to those in infinite horizon economies is also studied. It is shown that pointwise convergence always occurs for optimal consumption policies although it is unknown whether this occurs for optimal portfolio policies. Throughout this paper the authors assume that there are as many linearly independent risky securities as the dimension of the underlying uncertainty or, markets are dynamically complete. — The paper is very interesting and valuable.

Reviewer: G.Orman (Braşov)

### MSC:

60G40 | Stopping times; optimal stopping problems; gambling theory |

91B62 | Economic growth models |

60J60 | Diffusion processes |