Hattendorff Differential Equation for Multi-State Markov Insurance Models

• Main Authors: Rajeev Rajaram, Nathan Ritchey
• Format: Article
• Language: English
• Published: MDPI AG 2021-09-01
• Series: Risks
• Subjects: policy value; Kolmogorov forward equations; multistate model; Thiele’s differential equation; Hattendorff differential equation
• Online Access: https://www.mdpi.com/2227-9091/9/9/169

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 <i>t</i> random variable given that the state at time <i>t</i> is <i>j</i>, for a multistate Markov insurance model (denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>2</mn></msup><msubsup><mi>σ</mi><mi>t</mi><mrow><mo>(</mo><mi>j</mi><mo>)</mo></mrow></msubsup></mrow></semantics></math></inline-formula>). We also show using matrix notation that both models can be easily adapted for use in MATLAB for numerical computations.