Asymptotic analysis Catástrofes naturales Costs of the band strategies Cumulative process of customer demand Diffusion approximation Dividendos Ecuación de Hamilton-Jacobi-Bellman Expected discounted cumulative costs Financial mathematics Función de valor óptimo HJB equation Hamilton-Jacobi-Bellman equation Insurance Matemáticas Financieras Natural Catastrophe Optimal reinsurance Optimizacion Portfolio Management Probability Probability of drawdown Production-inventory control model Scaled Cram´er-Lundbergmodel Storage maximum capacity Variational inequalities optimal dividends ratcheting viscosity solution