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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.15175 |
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| _version_ | 1866911324106129408 |
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| author | Cho, Wonchan |
| author_facet | Cho, Wonchan |
| contents | I study intertemporal hedging demand in a continuous-time multi-asset long-run risk (LRR) model under Epstein--Zin (EZ) recursive preferences. The investor trades a risk-free asset and several risky assets whose drifts and volatilities depend on an Ornstein--Uhlenbeck type LRR factor. Preferences are described by EZ utility with risk aversion $R$, elasticity of intertemporal substitution $ψ$, and discount rate $δ$, so that the standard time-additive CRRA case appears as a limiting benchmark.
To handle the high-dimensional consumption--investment problem, I use a projected Pontryagin-guided deep policy optimization (P-PGDPO) scheme adapted to EZ preferences. The method starts from the continuous-time Hamiltonian implied by the Pontryagin maximum principle, represents the value and costate processes with neural networks, and updates the policy along the Hamiltonian gradient. Portfolio constraints and a lower bound on wealth are enforced by explicit projection operators rather than by adding ad hoc penalties.
Three main findings emerge from numerical experiments in a five-asset LRR economy: \textbf{(1)} the P-PGDPO algorithm achieves stable convergence across multiple random seeds, validating its reliability for solving high-dimensional EZ problems; \textbf{(2)} wealth floors materially reduce hedging demand by limiting the investor's ability to exploit intertemporal risk-return tradeoffs; and \textbf{(3)} the learned hedging portfolios concentrate exposure in assets with high correlation to the LRR factor, confirming that EZ agents actively hedge long-run uncertainty rather than merely following myopic rules. Because EZ preferences nest time-additive CRRA in the limit $ψ\to 1/R$, I use CRRA as an explicit diagnostic benchmark and, when needed, a warm start to stabilize training in high dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intertemporal Hedging Demand under Epstein-Zin Preferences in a Multi-Asset Long-Run Risk Model: Evidence from Projected Pontryagin-Guided Deep Policy Optimization Cho, Wonchan Systems and Control Optimization and Control I study intertemporal hedging demand in a continuous-time multi-asset long-run risk (LRR) model under Epstein--Zin (EZ) recursive preferences. The investor trades a risk-free asset and several risky assets whose drifts and volatilities depend on an Ornstein--Uhlenbeck type LRR factor. Preferences are described by EZ utility with risk aversion $R$, elasticity of intertemporal substitution $ψ$, and discount rate $δ$, so that the standard time-additive CRRA case appears as a limiting benchmark. To handle the high-dimensional consumption--investment problem, I use a projected Pontryagin-guided deep policy optimization (P-PGDPO) scheme adapted to EZ preferences. The method starts from the continuous-time Hamiltonian implied by the Pontryagin maximum principle, represents the value and costate processes with neural networks, and updates the policy along the Hamiltonian gradient. Portfolio constraints and a lower bound on wealth are enforced by explicit projection operators rather than by adding ad hoc penalties. Three main findings emerge from numerical experiments in a five-asset LRR economy: \textbf{(1)} the P-PGDPO algorithm achieves stable convergence across multiple random seeds, validating its reliability for solving high-dimensional EZ problems; \textbf{(2)} wealth floors materially reduce hedging demand by limiting the investor's ability to exploit intertemporal risk-return tradeoffs; and \textbf{(3)} the learned hedging portfolios concentrate exposure in assets with high correlation to the LRR factor, confirming that EZ agents actively hedge long-run uncertainty rather than merely following myopic rules. Because EZ preferences nest time-additive CRRA in the limit $ψ\to 1/R$, I use CRRA as an explicit diagnostic benchmark and, when needed, a warm start to stabilize training in high dimensions. |
| title | Intertemporal Hedging Demand under Epstein-Zin Preferences in a Multi-Asset Long-Run Risk Model: Evidence from Projected Pontryagin-Guided Deep Policy Optimization |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2512.15175 |