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Optimal consumption under deterministic income. (English) Zbl 1305.49034
From the Abstract: “We consider an individual or household endowed with an initial wealth, having an income and consuming goods and services. The wealth development rate is assumed to be a deterministic continuous function of time. The objective is to maximize the discounted consumption over a finite time horizon”.
From the Introduction: “The contribution of the present paper is in establishing a novel algorithm that allows to determine a closed-form expression for the value function and the optimal strategy. The basic idea of the algorithm is a systematic balancing of immediate consumption and of the future evolution of the system”.
To this purpose, the authors first prove the existence and uniqueness of the solution of the Hamilton-Jacobi equation in the viscosity sense, also using the concept of discontinuous viscosity solutions by the lower and upper semi-continuous envelopes.

49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49N90 Applications of optimal control and differential games
Full Text: DOI
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