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arXiv · 2607.22536

Optimal Investment with Switching Preferences

Yu-Jui Huang·Liviu Ignat·Traian A. Pirvu·Reihaneh Vafadar
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Abstract

Major life events can significantly increase individuals' risk aversion over a sustained period of time, as empirical studies reveal. How such an event-triggered shift of risk preferences impacts optimal investment is the focus of this paper. On a finite time horizon where a major life event may occur independently of the financial market, an investor aims to maximize her expected utility from terminal wealth while foreseeing a potential change in her risk aversion. We find that the associated Hamilton--Jacobi--Bellman (HJB) equation involves the post-event optimal value function (under elevated but fixed risk aversion after the event's occurrence), and the Fenchel--Legendre transform fails to linearize this HJB equation: it yields a parabolic equation with a fully nonlinear term, induced precisely by the post-event optimal value function. Through a combination of fixed-point, compactness, and verification arguments, we establish the existence of a positive convex classical solution with suitable growth to the fully-nonlinear parabolic equation. The convex conjugate of this solution is shown to satisfy the HJB equation and coincides with the pre-event optimal value function. The optimal trading strategy is obtained by concatenating the optimal pre-event and post-event strategies -- the former is expressed in terms of the solution to the HJB equation and the latter is traditional Merton's ratio.

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Yu-Jui Huang, Liviu Ignat, Traian A. Pirvu, Reihaneh Vafadar. 2026-04-20. Optimal Investment with Switching Preferences. https://arxiv.org/abs/2607.22536

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