Optimal dividend and proportional reinsurance strategy under standard deviation premium principle (Q2117578)

The authors do provide the classical optimal control scheme of Hamilton-Jacobi-Bellman, in order to determine the claims' obtained by a reinsurance company. The reinsurance contraction is supposed to be proportional one and the aim is to determine the optimal proportion of the inter-temporal claims obtained by the reinsurance company. The authors suppose that the surplus process is ``approximately'' described by a stochastic differential equation, with respect to some Brownian motion. The authors propose that the objective of the insurance company is to determine the optimal equity policy through the standard deviation premium principle.