On the use of intertemporal models to analyse how post-loss and post no-loss insurance demands differ

A general problem in insurance economics is to establish how insurance demand is affected by the size of the loss suffered in the previous period. This problem lays out the underlying objective of this study, which examines how insurance demand changes post-catastrophes, and how it can be theoretically modelled. We present a basic theoretic model to examine how post-accident insurance demand differs from post no-accident insurance demand. Our study first explores post-loss insurance demand from a two-period perspective and then examines how utility curvature parameters affect insurance demand across two periods. In our simulation results, it is observed that the optimal insurance demand with or without intertemporal consideration is the same in the absence of consumption smoothing mechanism. In addition, the experience of having an accident increases insurance purchases in the next period compared to when there was no accident in the previous period. In view of our findings, insurance stakeholders can develop strategies designed to improve post-loss outcomes for insurance consumers that include adequate coverage both after a loss and following a no-loss event by better understanding how insurance demand changes post-loss. We note that our proposition is limiting, but this limitation offers an interesting area of exploration. More studies are thus encouraged to model explicitly the utility derived from the wealth in the second period. In addition, further research is needed into the effects of consumption decisions and how to solve the bivariate optimisation problem that results.