Stochastic Risk Networks : Modeling, Analysis and Efficient Monte Carlo

We propose an insurance network model that allows to deal with default contagion risks with a particular aim of capturing cascading effects at the time of defaults. We capture these effects by finding an equilibrium allocation of settlements which can be found as the unique optimal solution of an optimization problem. This equilibrium allocation recognizes 1) the correlation among the risk factors, 2) the contractual obligations, which are assumed to follow popular contracts in the insurance industry (such as stop-loss), and 3) the interconnections of the insurance-reinsurance network. We are able to obtain an asymptotic description of the most likely ways in which the default of a specific group of participants can occur, by means of solving a multidimensional Knapsack integer programming problem. Finally, we propose a class of strongly efficient estimators (in a precise large deviations sense) for computing the expected loss of the network conditioning on the failure of a specific set of companies of companies