In this paper we study a continuous-time asset-allocation problem for a insurance firm that backs up the liabilities raised by the insurance contracts with the underwriting profits and the income resulting from investing in the financial market. Using the martingale approach and convex duality techniques we characterize strategies that maximize expected utility from final wealth under CRRA preferences when the firm have only a class of insurance. We present numerical results for some distributions of claims/liabilities with policy limit.
