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

Abstract

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.

Keywords:

• Intertemporal model
• insurance demand
• post-catastrophe
• optimal insurance

Public interest statement

The focus of this study is to examine the effects generated by disaster experience from an insurance demand-side standpoint and deduce a plausible reason why insurance demand may change after a catastrophic event. The paper aims to demonstrate how agents can maintain or modify insurance demand after the occurrence of a loss or no-loss event based on a theoretic model. This is done by an in-depth analysis and discussion of the performance of an insurance model that examines insurance demand changes after a loss event experience. The results show that having an accident increases insurance purchases in the next period compared to when there was no accident in the preceding period. One significant implication of our results is that a better understanding of how insurance demand changes post-loss experience and what kinds of behavioural factors drive these outcomes can help stakeholders (such as insurance companies, agents, governments, and consumers) develop educational programs and strategies to help improve post-loss outcomes for insurance consumers.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. If the contracts were actuarially fair, the insured would only purchase full coverage always. We need, therefore, that the contracts be actuarially unfair, or in other words, that they offer positive expected profit to the insurer.

Additional information

Funding

R. K. Mumo acknowledges the financial support from BIUST under grant number Botswana International University of Science and Technology <#AWARD-ID;>R00132</#AWARD-ID;></#AWARD-ID;>.

Notes on contributors

Richard Mumo

Richard Mumo is a Lecturer in Financial Mathematics at Botswana International University of Technology. His research interests focuses on the economics of natural disaster risk management, insurance product pricing, actuarial science and financial modelling, climate risk and adaptation, and climate finance.

John Boscoh H. Njagaraha

John Boscoh H. Njagaraha is a Lecturer in Mathematical Modelling at Botswana International University of Technology. His research focuses on applied mathematics in general, with particular emphasis on the applications of dynamical systems to infectious disease dynamics, substance abuse, and other biological systems.

Mercy K. Kiremu

Mercy K. Kiremu is a Management Accountant at the Waikato District Health Board. She previously worked as a lecturer in accounts and finance at the Western Institute of Technology at Taranaki. Her research interests and areas of expertise include climate finance, climate risk, financial risk, governance, and assurance.

Richard Watt

Richard Watt is a Professor of Economics at the University of Canterbury. His research focuses on applied microeconomics generally, with particular emphasis on the economic theory of risk bearing and the economics of copyright.