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In this paper we study the asymptotic decay of finite time ruin probabilitiesfor an insurance company that faces heavy-tailed claims, uses predictableinvestment strategies and makes investments in risky assets whose prices evolveaccording to quite general semimartingales. We show that the ruin problemcorresponds to determining hitting probabilities for the solution to a randomlyperturbed stochastic integral equation. We derive a large deviation result forthe hitting probabilities that holds uniformly over a family of semimartingalesand show that this result gives the asymptotic decay of finite time ruinprobabilities under arbitrary investment strategies, including optimalinvestment strategies.

Ruin probabilities under general investments and heavy-tailed claims