We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Optimal consumption and investment with welfare constraints.
- Authors
Jeon, Junkee; Kwak, Minsuk
- 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.
- Subjects
EXPECTED utility; UTILITY functions; RISK aversion; SUBSIDIES; VALUE (Economics)
- Publication
Finance & Stochastics, 2024, Vol 28, Issue 2, p391
- ISSN
0949-2984
- Publication type
Article
- DOI
10.1007/s00780-024-00529-1