A Continuous Time Framework for Sequential Goal-Based Wealth Management

Agostino Capponi () and Yuchong Zhang ()
Additional contact information
Agostino Capponi: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Yuchong Zhang: Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5G 1Z5, Canada

Management Science, 2024, vol. 70, issue 11, 7664-7691

Abstract: We develop a continuous time framework for sequential goals-based wealth management. A stochastic factor process drives asset price dynamics and the client’s goal amount and income. We prove the weak dynamic programming principle for the value function of our control problem, which we show to be the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We develop an equivalent and computationally efficient representation of the Hamiltonian, which yields the optimal portfolio within a factor-dependent opportunity set defined by the maximum and minimum variance hypersurfaces. Our analysis shows that it is optimal to fund an expiring goal up to the level where the marginal benefit of additional fundedness is exceeded by the opportunity cost of diverting wealth from future goals. An all-or-nothing investor is more risk averse toward an approaching goal deadline if well funded, but more risk seeking if not on track with upcoming goals, compared with an investor with flexible goals.

Keywords: dynamic programming; optimal control; finance: portfolio; mathematics; convexity (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.2022.02047 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:11:p:7664-7691

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().