In this paper, we consider the robust portfolio selection problem for an insurer in the sense of maximizing the exponential utility of his wealth. This special robust investment problem, where underwriting results and a risk-free asset are considered, differs from ordinary robust portfolio selection problems. The insurer has the option of investing in a risk-free asset and multiple risky assets whose returns are described by the factor model. The rate of underwriting return is also assumed to be correlated with returns of risky assets. When the parameters are perturbed in a joint uncertainty set, the robust investment problem for an insurer is established and this problem is reformulated and solved as a cone programming problem. Finally, some computational results are given for raw market data.
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