<p>Catastrophe bonds (CAT bonds) are the prominant category of insurance-linked securities that transfer insured risk from insurance and reinsurance entities to the capital market. The unique risk characteristics of these bonds enable financial institutions to employ them in their portfolios for hedging and risk management, differentiating them from other bond types. For hedging and other trading purposes, it is crucial to determine the rate at which bond prices change in relation to the underlying asset’s price and other related parameters. This paper’s primary objective is to establish a CAT bond pricing model utilizing the partial differential equations (PDE) method, wherein the bonds price is a function of the interest rate, PCS index, and the passage of time. Therefore, the variation in the bond’s value is influenced by changes in the interest rate and the loss ratio.We model bond prices using portfolio management strategies and stochastic processes for interest rates (jump diffusion model) and loss ratios (CIR process). Our alternative portfolio employs the loss ratio as the underlying instrument, resulting in a PIDE through stochastic modeling, hedging, and the no-arbitrage principle in an incomplete market. So, the dynamics of bond prices are determined by this PIDE, concerning initial and boundary conditions, and solving this complex equation requires advanced numerical methods because no closed-form solution is suggested. Also, aligning our model parameters with the price of the CAT bond is other objective so as to have a pricing function that can not be achieved through the numerical tecnique. So, the advancements in using Artificial Neural Networks to solve partial differntial equation have led us to apply this approach. Artificial Neural Networks provide continuous and differentiable solutions over the entire domain, eliminating the requirement for a predefined mesh, unlike the traditional numerical technique. We utilize the Physics-Informed Neural Network because the problem can be solved in an unsupervised manner by integrating the partial differntial equation into the neural network. Also, a pricng function can be built by setting up all parameters of the model as input instead of just being variables of the bond function, as used in the primary Physics-Informed Neural Network. Differentiating this function with respect to the model parameters allows for the sensitivity analysis that is one application for this map. Furthermore, it can facilitate future works, including calibration tasks that can be perceived as an inverse problems. Finally, the Physics-Informed Neural Networks are able to learn from new data whenever the updated parameters enter the model, meaning that the framework can be used for diverse problems in this field.</p>