Ricerc@Sapienza

We consider the investment problem for a non-life insurance company seeking to minimize the ruin probability. Its reserve is described by a perturbed risk process possibly correlated with the financial market. Assuming exponential claim size, the Hamilton-Jacobi-Bellman equation reduces to a first order nonlinear ordinary differential equation, which seems hard to solve explicitly. We study the qualitative behavior of its solution and determine the Cramér-Lundberg approximation. Moreover, our approach enables to find very naturally that the optimal investment strategy is not constant.

We test whether adverse changes to banks’ market valuations during the financial and sovereign debt crises affected firms’ real decisions. Using new data linking over 5000 non-financial Italian firms to their bank(s), we find that increases in banks’ CDS spreads, and decreases in their equity valuations, resulted in lower investment, employment, and bank debt for younger and smaller firms. These effects dominate those of banks’ balance-sheet variables. Moreover, CDS spreads matter more than equity valuations.