Hattendorff Differential Equation for Multi-State Markov Insurance Models

Abstract

We derive a Hattendorff differential equation and a recursion governing the evolution of continuous and discrete time evolution respectively of the variance of the loss at time t random variable given that the state at time t is j, for a multistate Markov insurance model (denoted by 2σt(j)). We also show using matrix notation that both models can be easily adapted for use in MATLAB for numerical computations.

Keywords

• policy value
• Kolmogorov forward equations
• multistate model
• Thiele’s differential equation
• Hattendorff differential equation