Optimal Investment to Reach a Financial Goal: A Stochastic Control Framework

Gechun Liang, Moris S. Strub, Yuwei Wang and Zhaojun Yang

Papers from arXiv.org

Abstract: We develop a framework for an investor who trades until she either reaches a financial goal or an exogenous deadline arrives. Analogous to utility functions over wealth, we measure satisfaction with the timing of reaching a goal by a discount function. For a continuous-time market where a stochastic factor drives the dynamics of stock prices and the financial goals, the investor maximizes the expected discount at the goal reaching time and the expected utility of the funding ratio if the goal remains unreached by the deadline. This setup leads to a new class of stochastic control problems. We establish Bellman's principle of optimality and characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman equation. When the deadline is infinite and the goal is constant, the HJB equation reduces to a form related to the backward heat equation, for which we provide a complete characterization of smooth solutions. When analytical solutions are unavailable, we develop an approach based on Howard's algorithm to obtain numerical solutions. Our analysis shows that optimal investment policies for goal reaching problems can be decreasing in the drift of risky assets and need not converge to full risk-free investment even as volatility diverges to infinity.

Date: 2026-10
References: Add references at CitEc
Citations:

Downloads: (external link)
https://arxiv.org/pdf/2610.10046 Latest version (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:arx:papers:2610.10046

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().