Optimal investment under irreversible consumption and locally risk-seeking preferences

Seungwon Jeong; Junkee Jeon; Hyeng Keun Koo; Seungwon Jeong; Junkee Jeon; Hyeng Keun Koo

doi:10.3934/jimo.2026039

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 2: 1063-1086. doi: 10.3934/jimo.2026039

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Optimal investment under irreversible consumption and locally risk-seeking preferences

1.
Global-Learning & Academic Research Institution for Master's/PhD Students and Postdocs, Chonnam National University, Korea
2.
Department of Applied Mathematics, Kyung Hee University, Korea
3.
Department of Financial Engineering, Ajou University, Korea

Received: 31 October 2025 Revised: 20 December 2025 Accepted: 13 January 2026 Published: 26 January 2026
91G10, 93E20, 49L20, 60H30

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.
- irreversible (non-decreasing) consumption,
- consumption ratcheting,
- non-concave utility,
- Friedman–Savage preferences,
- free-boundary analysis,
- portfolio optimization,
- concave-hull method,
- ratcheted guarantees
Citation: Seungwon Jeong, Junkee Jeon, Hyeng Keun Koo. Optimal investment under irreversible consumption and locally risk-seeking preferences[J]. Journal of Industrial and Management Optimization, 2026, 22(2): 1063-1086. doi: 10.3934/jimo.2026039

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Abstract

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.

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