Optimal investment under irreversible consumption and locally risk-seeking preferences

We study an infinite-horizon portfolio choice problem in which an investor cannot tolerate any decline in consumption. The agent also exhibits locally risk-seeking preferences of the Friedman–Savage type, which generate alternating regions of risk aversion and risk loving. The interaction between the non-decreasing consumption constraint and local risk-seeking behavior produces an extreme form of habit formation and yields a dynamic free-boundary structure.To address the resulting non-concave optimization problem, we transform it into an equivalent concave problem via the concave-hull technique and characterize the optimal consumption and portfolio policies in closed form. The optimal policy features delayed consumption adjustments even when wealth is sufficient to remain within the risk-seeking region, followed by a discrete jump in consumption once a critical threshold is reached. The optimal portfolio displays trend-chasing behavior: risky exposure is higher during booms, while allocation becomes investor conservative after upward consumption adjustments.Numerical simulations illustrate that the expected duration of the risk-seeking regime increases with the investor patience, the magnitude of the consumption jump, and the market risk premium. Finally, the model admits an actuarial interpretation: the non-decreasing consumption rule parallels ratcheted or guaranteed-increasing payouts in insurance and annuity products, providing a theoretical foundation for analyzing dynamic guarantee and bonus-adjustment mechanisms.