Empirical tail risk management with model-based annealing random search

Tail risk measures such as Value at Risk (VaR) and Conditional Value at Risk (CVaR) are popularly accepted criteria for financial risk management, but are usually difficult to optimize. Especially for VaR, it generally leads to a non-convex NP-hard problem which is computationally challenging. In this paper we propose the use of model-based annealing random search (MARS) method in tail risk optimization problems. The MARS, which is a gradient-free and flexible method, can widely be applied to solving many financial and insurance problems under mild mathematical conditions. We use a weather index insurance design problem with tail risk measures including VaR, CVaR and Entropic Value at Risk (EVaR) as the objective function to demonstrate the viability and effectiveness of MARS. We conduct an empirical analysis in which we use a set of weather variables to hedge against corn production losses in Illinois. Numerical results show that the proposed optimization scheme effectively helps corn producers to manage their tail risk.