Geometric Compound Hawkes Process and its Applications in Finance

The authors introduce a new model for a stock price, namely, geometric compound Hawkes process, and show how this model can be applied to solving many problems in finance, including European and American option pricing (perpetual American options), and Merton portfolio optimization problem. This model is a generalization of some well-known models in finance, such as Cox-Ross-Rubinstein model (1976) (geometric binomial process), Aase model (1988) (geometric compound Poisson process) and geometric Markov renewal model (2013). numerical examples are presented as well