SVM-Jacobi for fitting linear combinations of exponential distributions with applications to finance and insurance

We propose a method called SVM-Jacobi to approximate probability distributions by linear combinations of exponential distributions, associated with a comprehensive asymptotic analysis. In multivariate cases, the multivariate distribution is approximated by linear combinations of products of independent exponential distributions, and the method works effectively. The proposed method has many applications in both quantitative finance and insurance, especially for modeling random time, like default time and remaining lifetime. In addition to the methodology and theoretical analysis, we provide examples of pricing defaultable bonds, European options, credit default swaps, equity-linked death benefits, and calculating the credit value adjustment of credit default swaps. Finally, some numerical results based on real data and simulated data are presented for illustration.