Abstract
In this paper we consider an investment problem by an insurance firm. As in the classical model of collective risk, it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. We introduce a conversion mechanism of funds from cash into investments and vice versa. Contrary to the conventional collective risk model we do not assume a ruin barrier. Instead we introduce conversion costs to account for the problems implicit in reaching the zero boundary. The objective of the firm is to maximize its net profit by selecting an appropriate investment strategy. A diffusion approximation is suggested in order to obtain tractable results for a general claim size distribution.
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