Disaster Risk and a Household’s Dynamic Asset-Formation Behavior: Jump Control Model of Household

This study formulates a dynamic model of a household’s asset-formation process under stochastic arrivals of disasters. If the disaster risk is catastrophic, then the disaster insurance market cannot spread the risk completely, and the insurance premium will include additional loadings, namely, risk premiums. The study reports that, under such a market condition, the representative household does not purchase an insurance that fully covers its potential losses, resulting in a non-smooth asset-formation path that is associated with downward jumps at times of disaster. It concludes that the benefit of disaster mitigation investment is thus composed of an “ex ante accumulation effect” and an “ex post mitigation effect.” The dynamic problem of a household’s asset formation is characterized by the jump control problem related to insurance contracts. Moreover, the problem is associated with a recursive structure where a phase of recovery from one disaster is simultaneously a phase of preparedness for the next disaster that randomly arrives; thus, extra attention is given to optimal resource allocation between reconstruction and risk management. The jump control model can be a new standard mathematical framework of household resilience.