Optimal consumption and investment with welfare constraints

Junkee Jeon () and Minsuk Kwak ()
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Junkee Jeon: Kyung Hee University
Minsuk Kwak: Hankuk University of Foreign Studies

Finance and Stochastics, 2024, vol. 28, issue 2, No 4, 451 pages

Abstract: Abstract This paper investigates an optimal consumption and investment problem of an economic agent who faces a welfare constraint: the agent does not accept her expected utility (continuation value) to fall below a certain fixed level regardless of the time and state. This optimisation problem involves an infinite number of constraints. Using a duality approach, we transform infinitely many constraints into a single constraint and define a dual problem, which becomes a two-dimensional singular control problem. The dual problem provides its associated Hamilton–Jacobi–Bellman (HJB) equation with a gradient constraint. Under a general class of utility functions, we obtain an explicit solution to the HJB equation and provide optimal strategies by establishing a duality theorem. As an example, we consider hyperbolic absolute risk aversion (HARA) utility which may incorporate a government subsidy or basic support, and provide its solutions and implications.

Keywords: Consumption and investment; Welfare constraints; General utility; Singular control problem; Duality approach; Dynamic constraints; 91G10; 93E20; 91B08 (search for similar items in EconPapers)
JEL-codes: C61 G11 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-024-00529-1

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