  We study a reinsurance Stackelberg game in which both the insurer and the
reinsurer adopt the mean-variance (abbr. MV) criterion in their decision-making
and the reinsurance is irreversible. We apply a unified singular control
framework where irreversible reinsurance contracts can be signed in both
discrete and continuous times. The results theoretically illustrate that,
rather than continuous-time contracts or a bunch of discrete-time contracts, a
single once-for-all reinsurance contract is preferred. Moreover, the
Stackelberg game turns out to be centering on the signing time of the single
contract. The insurer signs the contract if the premium rate is lower than a
time-dependent threshold and the reinsurer designs a premium that triggers the
signing of the contract at his preferred time. Further, we find that
reinsurance preference, discount and reversion have a decreasing dominance in
the reinsurer's decision-making, which is not seen for the insurer.
