In this paper we study optimal investment strategies that maximize expected utility from consumption and terminal wealth in a pure-jump market model where the dynamics of asset prices follow a swithching process and the size of the jump and the trend are dependent on the waiting time between jumps, in addition, the trend is dependent on a dichotomous chain with values in the inter-arrival times. We show that the counting process associated to the arrival times has as compensator a Hazard function that is dependent on the inter-arrival times. This implies that the conditional expected value of the process solves a coupled system of Volterra equations of second kind. As an application, the GOP (growth-optimal portfo- lio) case is considered, where the Volterra system is solved by means of numerical methods in the particular cases in which the inter-arrival times are distributed as hyperexponential and Weibull.
