pricing cat bond under jump diffusion model

The main goal of this paper is to present a model based on pde approach for pricing catastrophe risk bonds (cat) and solve it in an appropriate way. firstly we assume that the interest rate has jump, so ‎we ‎have a‎ ‎jump ‎term ‎in the ‎model ‎of ‎cat ‎bond. also we suppose the ‎dynamic ‎of ‎loss ‎follows ‎cir ‎model. after using free arbitrage portfolio strategy and make it non-stochastic, we reach to a partial integral differential equation (pide) that is the cat bond price model. as there is no closed-form solution to be obtained, we want to solve our model numerically. to do so, we propose an alternative method based on radial basis functions (rbfs) to transfer the pde to system of ode's and finally we solve the system by runge kutta method.