A Continuous Time Framework for Sequential Goal-Based Wealth Management

63 Pages Posted: 3 Jun 2022 Last revised: 16 Oct 2023

See all articles by Agostino Capponi

Agostino Capponi

Columbia University - Department of Industrial Engineering and Operations Research

Yuchong Zhang

University of Toronto - Department of Statistics

Date Written: October 13, 2023

Abstract

We develop a continuous time framework for sequential goals-based wealth management.
A stochastic factor process drives asset price dynamics as well as 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 towards an approaching goal deadline if she is well funded, but more
risk seeking if she is not on track with upcoming goals, compared to an investor with
flexible goals.

Keywords: goal based wealth management, funding ratios, dynamic programming, consumption

JEL Classification: G11, G40

Suggested Citation

Capponi, Agostino and Zhang, Yuchong, A Continuous Time Framework for Sequential Goal-Based Wealth Management (October 13, 2023). Available at SSRN: https://ssrn.com/abstract=4121931 or http://dx.doi.org/10.2139/ssrn.4121931

Agostino Capponi (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research ( email )

Yuchong Zhang

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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