  This paper presents some new results on Parisian ruin under Levy insurance
risk process, where ruin occurs when the process has gone below a fixed level
from the last record maximum, also known as the high-water mark or drawdown,
for a fixed consecutive periods of time. The law of ruin-time and the position
at ruin is given in terms of their joint Laplace transforms. Identities are
presented semi-explicitly in terms of the scale function and the law of the
Levy process. They are established using recent developments on fluctuation
theory of drawdown of spectrally negative Levy process. In contrast to the
Parisian ruin of Levy process below a fixed level, ruin under drawdown occurs
in finite time with probability one.
