  In this paper, we study the ruin problem with investment in a general
framework where the business part X is a L{\'e}vy process and the return on
investment R is a semimartingale. We obtain upper bounds on the finite and
infinite time ruin probabilities that decrease as a power function when the
initial capital increases. When R is a L{\'e}vy process, we retrieve the
well-known results. Then, we show that these bounds are asymptotically optimal
in the finite time case, under some simple conditions on the characteristics of
X. Finally, we obtain a condition for ruin with probability one when X is a
Brownian motion with negative drift and express it explicitly using the
characteristics of R.
