A Markov chain approach to model reconstruction

Abstract

Motivated by the fact that Chile is one of the most seismically active countries in the world (located over the ‘Pacific Ring of Fire’), we define a methodology for estimating the cost of housing reconstruction by modelling the occurrence of natural disasters as a Markov chain. Specifically, the states of the chain correspond to the different possible conditions of the housing infrastructure and the transition probabilities represent the possibility of change from one condition to another once the disaster has occurred. We prove that for the case of the 2010 Chilean earthquake, the matrix representing the process admits a stationary state vector. Using this vector, which we interpreted as the portion of time that the chain spends in each state in the long term, we define a cost function associated with total reconstruction. If this cost function is continuous, then this methodology allows policymakers to make decisions when facing the trade-off between current partial reconstruction and future total reconstruction.