  In this paper, we consider risk-sensitive discounted control problem for
continuous-time jump Markov processes taking values in general state space. The
transition rates of underlying continuous-time jump Markov processes and the
cost rates are allowed to be unbounded. Under certain Lyapunov condition, we
establish the existence and uniqueness of the solution to the
Hamilton-Jacobi-Bellman (HJB) equation. Also we prove the existence of optimal
risk-sensitive control in the class of Markov control.
