The impact of shareholders’ limited liability on risk- and value-based management

In this paper, we analyze the consequences of shareholders’ limited liability for the risk- and value-based investment decisions made by a nonlife insurer under solvency constraints. We consider an insurance company with shareholders who are not responsible for debts exceeding the amount of their stake. This insurer aims to maximize the shareholder value based on preference functions while simultaneously controlling for the ruin probability. We show that the optimal asset allocation given this limited liability is riskier in terms of the standard deviation and in terms of the corresponding ruin probability than in the case of full liability. Moreover, the limited liability sets an incentive to follow an investment strategy that exploits the maximum admissible ruin probability level and even to select inefficient risk–return combinations. Since the limited liability problem arises if customers cannot monitor the activity – or, more precisely, the solvency – level of the insurer, and thus cannot condition their demand based on the risk, this study emphasizes the importance of public reporting as required by the Solvency and Financial Condition Report of Solvency II