Two-dimensional forward and backward transition rates (Q6593139)

Through the paper, forward transition rates are extended in a useful way within the insurance framework, particularly for the market-consistent valuation of insurance liabilities. To follow up the study, the main characterizations of life insurance modeling are presented. Then, the paper focuses on defining the forward and backward transition rates in two dimensions and developing a corresponding integral equation, that generalizes Kolmogorov's forward equation. The study of the equations obtained is enhanced, with special attention to the uniqueness of the solution. The calculation of certain conditional moments of two-dimensional forward and backward transitions rates is provided, as well as the calculation of conditional variances. Finally, the calculation of path-dependent cash-flows is determined. Technical details can be found in the Appendix.