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.

Natural disasters generate great economic costs related to damaged houses or loss of infrastructure. In this context, the case of Chile is particularly interesting, as it is located in the "Pacific Ring of Fire" and is considered one of the most seismically active countries in the world. Based on the evidence from the 2010 earthquake, an empirical study was carried out using the panel survey CASEN Post earthquake. We model a Markov chain whose states represent housing conditions (good, regular and bad) and where each instance of the chain corresponds to the occurrence of an earthquake. For this model, we calculate the transition probabilities of moving from one state to another and find the stationary probabilities of the chain. We interpret these probabilities as the percentage of time that houses spend in each state in the long term. We propose a method to calculate the expected cost of full reconstruction of houses. This information could be useful to policy makers for evaluating if it is necessary to repair the damage or wait for the destruction of the house and rebuild it.