A biased-randomized algorithm for optimizing efficiency in parametric earthquake (Re) insurance solutions

Abstract

Natural catastrophes with their widespread damage can overwhelm the financial systems of large communities. Catastrophe insurance is a well-understood financial risk transfer mechanism, aiming to provide resilience in the face of adversity. However, catastrophe insurance has generally a low penetration, mainly due to its high cost or to distrust of the product in providing a fast financial recovery. Parametric insurance is a form of derivative insurance that pays quickly and transparently based on a few measurable features of the event, offering a promising avenue to increase catastrophe insurance coverage. In the context of seismic risk, parametric policies may use location and magnitude of an earthquake to determine whether a payment should be made. In this paper we follow a design typology referred to as ‘cat-in-a-box’, where magnitude thresholds are defined over a set of cuboids that partition Earth’s crust. The main challenge in the design of these tools consists in finding the optimal magnitude thresholds for a large set of cubes that maximize efficiency for the insured, subjected to a budgetary constraint. Additional geometric constraints aim to reduce the volatility of payments under uncertainty. The parametric design problem is a combinatorial problem, which is NP-hard and large scale. In this paper we propose a fast heuristic and a biased-randomized algorithm to solve large-sized problems in reasonably low computing times. Experimental results illustrate the computational limits and solution quality associated with the proposed approaches.