A note on Merton’s “Optimum consumption and portfolio rules in a continuous-time model”. (English) Zbl 0657.90028

In the paper “Optimum consumption and portfolio rules in a continuous- time model”, by R. C. Merton [ibid. 3, 373-413 (1971)], solutions obtained in cases when marginal utility at zero consumption is finite are not feasible. While they do satisfy the Hamilton-Jacobi Bellman equations, they do not represent appropriate value functions because the boundary behavior near zero wealth is not satisfactorily dealt with. In this note, we specify the boundary behavior and characterize optimal solutions.


91B62 Economic growth models
91B28 Finance etc. (MSC2000)
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