这篇论文揭示了灾难态本身就能产生前景理论行为，对做强化学习安全控制、风险决策建模的研究者很有启发，建议读一下推导和实验设计。
该研究在马尔可夫决策过程（MDP）中引入吸收灾难态，发现即使风险中性且无效用曲率，标准Bellman最优性仍会产生前景理论三大特征：S型价值函数（近灾难凸、远场凹）、内生损失厌恶系数λ*>1、以及反射效应策略反转。在495种配置下，正漂移（增长）场景中靠近灾难态时最优策略选择安全动作，负漂移（衰退）场景中则选择冒险动作。研究推导出渐近损失厌恶平台λ的闭式表达式，仅依赖胜率p、收益不对称比r和折扣因子β，与数值解拟合R²=0.999。该机制无需不对称收益，且现象在表格Q学习和随机转移下稳健存在。
Prospect-Theory Behavior from Bellman Optimality in MDPs with Catastrophic States
We study risk-neutral control in Markov decision processes with an absorbing catastrophic state. Even though rewards are linear and the agent has no utility curvature, probability weighting, or framing dependence, standard Bellman optimality produces three prospect-theory-like signatures: an S-shaped value-function profile (convex near catastrophe, concave in the far field), an endogenous loss-sensitivity coefficient $λ^*(S) > 1$, and a reflection-effect policy reversal. Across 495 configurations, the optimal policy plays safe near catastrophe in positive-drift (growth) regimes despite the risky action's higher immediate expected value, and plays risky near catastrophe in negative-drift (decline) regimes despite the safe action's lower immediate expected loss. We derive a closed-form expression for the asymptotic loss-aversion plateau $\barλ$ that depends only on win probability $p$, payoff asymmetry $r = |Δ_\ell/Δ_w|$, and discount factor $β$, and matches numerical solutions to $R^2 = 0.999$. The mechanism does not require asymmetric payoffs. Across a sweep of $(p,β)$ at three asymmetry levels, the asymmetry share of $\barλ$ above unity has median 4.6% at $r = 1.25$ and rises to 13.9% at $r = 2$, with the boundary contribution exceeding the asymmetry contribution in every cell tested. The phenomena persist under tabular Q-learning (a model-free agent reproduces $V^*$ at correlation 0.98 in growth and 1.00 in decline) and under stochastic transitions with Gaussian, heavy-tailed Student-$t_3$, and asymmetric skew-normal noise up to 50% of the step size, where the asymptotic plateau tracks the closed-form prediction within 0.41% for safe-channel noise and within 9.6% for risky-channel or both-channel noise. These results identify absorbing failure states as a sufficient structural mechanism for prospect-theory-like behavior under optimal control.