  We investigate the geometric properties of the convex hull over $n$
successive positions of a planar random walk, with a symmetric continuous jump
distribution. We derive the large $n$ asymptotic behavior of the mean
perimeter. In addition, we compute the mean area for the particular case of
isotropic Gaussian jumps. While the leading terms of these asymptotics are
universal, the subleading (correction) terms depend on finer details of the
jump distribution and describe a "finite size effect" of discrete-time jump
processes, allowing one to accurately compute the mean perimeter and the mean
area even for small $n$, as verified by Monte Carlo simulations. This is
particularly valuable for applications dealing with discrete-time jumps
processes and ranging from the statistical analysis of single-particle tracking
experiments in microbiology to home range estimations in ecology.
