  Motivated by a risk process with positive and negative premium rates, we
consider a real-valued Markov additive process with finitely many background
states. This additive process linearly increases or decreases while the
background state is unchanged, and may have upward jumps at the transition
instants of the background state. It is known that the hitting probabilities of
this additive process at lower levels have a matrix exponential form. We here
study the hitting probabilities at upper levels, which do not have a matrix
exponential form in general. These probabilities give the ruin probabilities in
the terminology of the risk process. Our major interests are in their analytic
expressions and their asymptotic behavior when the hitting level goes to
infinity under light tail conditions on the jump sizes. To derive those
results, we use a certain duality on the hitting probabilities, which may have
an independent interest because it does not need any Markovian assumption.
