  In this paper we study the asymptotic decay of finite time ruin probabilities
for an insurance company that faces heavy-tailed claims, uses predictable
investment strategies and makes investments in risky assets whose prices evolve
according to quite general semimartingales. We show that the ruin problem
corresponds to determining hitting probabilities for the solution to a randomly
perturbed stochastic integral equation. We derive a large deviation result for
the hitting probabilities that holds uniformly over a family of semimartingales
and show that this result gives the asymptotic decay of finite time ruin
probabilities under arbitrary investment strategies, including optimal
investment strategies.

Risk Management;Probability