Fahrenwaldt M. Sensitivity of life insurance reserves via Markov semigroups. Scandinavian Actuarial Journal. We consider Thiele’s differential equation for the reserve of a multi-state insurance contract with functional dependence on the surplus. In an analytic approach based on semigroups, we obtain existence and uniqueness results and prove growth and regularity properties. Moreover, we investigate the sensitivity of the reserves with respect to the surplus, payment rate, and transition assumptions in terms of uniform and pointwise estimates. The approach can easily be generalized.