The Mathematical Survival Collapse: A Formal Proof of Prospect Theory’s Failure in Non-ergodic Environments

This paper provides a formal mathematical critique of the normative foundations of Prospect Theory (PT) and Expected Utility Theory (EUT). We argue that modern decision theory commits a fundamental ontological fallacy: treating non-ergodic survival processes as if they were ergodic ensemble gambles. By modeling human existence as a multiplicative, 8-dimensional life-state space (encompassing physical, financial, and emotional capitals), we utilize Itô calculus to prove that the "Ensemble Average" (expected value) necessarily diverges from the "Time Average" experienced by an individual trajectory. Our formal proof demonstrates that maximizing ensemble averages leads to a cumulative "volatility penalty" ($-\sigma^2/2$), which, in the presence of absorbing barriers, results in "statistical suicide"—the inevitable collapse of the individual system over an infinite time horizon. Consequently, we propose a radical reinterpretation of behavioral "biases." We show that loss aversion and status quo bias are not irrational cognitive failures, but are instead mathematically optimal stochastic control strategies designed to maximize time-average growth rates and ensure existential survival. This work establishes "survival" as the primary axiom of decision mathematics, shifting the paradigm from static utility maximization to dynamic ergodicity economics.