  We rigorously investigate closed Minkowski/Finsler billiard trajectories on
$n$-dimensional convex bodies. We outline the central properties in comparison
and differentiation from the Euclidean special case and establish two main
results for length-minimizing closed Minkowski/Finsler billiard trajectories:
one is a regularity result, the other is of geometric nature. Building on these
results, we develop an algorithm for computing length-minimizing closed
Minkowski/Finsler billiard trajectories in the plane.
