Merton Investment Problems in Finance and Insurance for the Hawkes-based Models

Abstract: We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) of an insurance company with the amount of claims described by the risk model based on GCHP. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.