×

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.

MSC:

91B62 Economic growth models
91B28 Finance etc. (MSC2000)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Karatzas, I; Lehoczky, J; Sethi, S; Shreve, S, Explicit solutions of a general consumption/investment problem, Math. oper. res., 11, 261-294, (1986) · Zbl 0622.90018
[2] Merton, R.C, Optimum consumption and portfolio rules in a continuous-time model, J. econ. theory, 3, 373-413, (1971) · Zbl 1011.91502
[3] Merton, R.C, Erratum, J. econ. theory, 6, 213-214, (1973)
[4] Merton, R.C, Lifetime portfolio selection under uncertainty: the continuous-time case, Rev. econ. statist., 51, 247-257, (1969)
[5] Sethi, S.P; Taksar, M, Optimal consumption and investment policies with bankruptcy modelled by a diffusion process with delayed reflection, (), 267-269
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.