Portfolio Choice with Competing Precautionary and Accumulation Goals

2026-06-02

AI Summary

This study addresses the optimal investment and contribution strategies for households facing both stochastic deadline targets—such as medical emergencies—and fixed deadline goals—like retirement or tuition payments—in a Black-Scholes market. Under mandatory and voluntary contribution schemes, the authors employ continuous-time dynamic programming and stochastic control to maximize the weighted sum of probabilities of fully achieving both types of objectives. The analysis uncovers two key phenomena arising from multi-goal interactions: a “growth crowding-out effect” and a “deadline pressure effect.” Notably, household wealth exhibits a non-monotonic relationship with the value function, and the flexibility of voluntary contributions proves most valuable at intermediate wealth levels. The work further quantifies ex-ante and terminal option values, offering a novel theoretical foundation for multi-objective financial planning.

Abstract

We study optimal portfolio choice for a household simultaneously managing a random-deadline goal, such as a medical emergency or job loss, and a fixed-deadline goal such as retirement or college tuition. Under a forced funding rule, in which each goal is paid in full whenever affordable, the household maximizes a weighted sum of the probabilities of fully funding both goals in a Black--Scholes market. We identify two novel effects absent from single-goal models: a growth crowding-out effect, in which precautionary saving for the random goal distorts investment toward the fixed goal, and a deadline pressure effect, in which a compressed saving horizon forces excess risk-taking. A striking implication is that the value function need not be monotone in wealth: a household just above the random-goal threshold is forced to pay it when the shock arrives, depleting its wealth for the fixed goal, and ends up worse off than a slightly poorer household that missed the random goal but kept its wealth intact. This non-monotonicity is absent from all single-goal benchmarks and arises purely from the interaction between the two goal types under forced funding. We further study an optional funding variant in which the household may decline the fixed-deadline goal at time $T$ rather than being required to fund it. We characterize the ex ante option value, i.e., the full time-$0$ value of this flexibility and the terminal option value, i.e., its value at the funding decision node. We find that both options are most valuable at intermediate wealth levels where paying the fixed-deadline goal would substantially reduce the continuation value of the random-deadline problem.

Problem

• portfolio choice
• competing goals
• precautionary saving
• fixed-deadline goal
• random-deadline goal

Innovation

• portfolio choice
• competing goals
• precautionary saving
• forced funding
• non-monotonic value function