The Talebian Architecture of Survival in Nonlinear Markets: The Clock of Regimes Model*

Abstract

Oscar Linares and Ricards Bulavs

This paper introduces the Clock of Regimes (COR) model, a new class of regime-switching model characterized by the N = −K⁻¹ operator. In a conventional Hidden Markov Model (HMM), persistence is encoded implicitly in the diagonal elements of the transition matrix A, the a_ii. A large value of aii indicates that regime i tends to persist, but this representation captures only one-step persistence—the probability of remaining in the state at the next instant. It does not represent the cumulative temporal probability mass generated by remaining there. Under the HMM, regime St evolves according to A, with implied expected spell length Eτ_i = 11−a_ii. If a_ii = 1, residence time becomes infinite and the process becomes structurally non-ergodic. Treating conditional persistence as permanence replaces stochastic dwell time with deterministic residence, suppressing regime uncertainty and hazard. In Talebian terms, conditional persistence is survival-compatible, whereas assumed permanence is ruin-compatible. The COR framework resolves this limitation by introducing an exit parameter ε ∈ 0,1, Q = 1−εA, which converts the HMM into a transient system. This yields the fundamental matrix V¹ = I −Q ⁻¹, integrating expected state occupancy across the entire future horizon. COR therefore transforms transition probabilities into temporal mass, making regime duration and exposure structurally observable.

PDF