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R. Kovacevic, W. Semmler:
"Poverty traps and disaster insurance in a bi-level decision framework";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2020-02 (2020), 02; 25 pages.

In this paper we study mechanisms of poverty traps that can occurafter large disaster shocks. Our starting point is a stylized deterministic dynamicmodel with locally increasing returns to scale possibly generating multiple equilib-ria paths wit finite upper equilibrium. The deterministic dynamics is then over-layed by random dynamics where catastrophic events happen at random pointsof time. The number of events follows a Poisson process, whereas the propor-tional capital losses (given a catastrophic event) are beta distributed. In a setupwith fixed insurance premium per unit of insured capital, a fraction of the capitalmight be insured, and this fraction may change after each event. We seek for anoptimal strategy with respect to the insured fraction. Falling below the instableequilibrium of the deterministic dynamics introduces the possibility of ending upin a poverty trap after the disaster shocks. We show that the trapping probability(over an infinite time horizon) is equal to one when the stable upper equilibrium ofthe deterministic dynamics is finite. This is true regardless of the chosen amountof insured capital. Optimization then is done with the expected discounted capitalafter the next catastrophic event as the objective. Our model may also be usefulto assess risk premia and creditworthiness of borrowers when a sequence of shocksat uncertain times and of uncertain size occurs.

https://publik.tuwien.ac.at/files/publik_289698.pdf