Mathematical model of earthquake bond for managing financial risk caused by earthquake

In our country, Japan, it is urgent to mitigate the risk caused by a big earthquake. We propose an earthquake bond issued by the government. Our main objective is to propose its mathematical model to decide its interest rate and guaranteed principal rate. In order to do this, we first introduce several assumptions about market and investors, and set up scenarios about a big earthquake. Based on these assumptions, we formulate an optimization problem to obtain alternatives of earthquake bonds with the proper set of an interest rate and guaranteed principal rate. Then, we construct a decision making model for the government. In this model, the government evaluates alternatives by a value function under risk. Finally, we present numerical examples based on the case of the Hanshi-Awaji Earthquake.