Optimal Consumption Problem in a Diffusion Short-Rate Model

Details Optimal Consumption Problem in a Diffusion Short-Rate Model Optimal Consumption Problem in a Diffusion Short-Rate Model

2009-10-02

arxiv.org/abs/0910.0378v1

Mathematics

Optimization and Control

36 pages, 2 figures

Scientific paper

We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.

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