Stochastic Cash Flows and Backward Semi-Markov Reward
Processes
Raimondo Manca
University La Sapienza, Rome
A full treatment of continuous time homogeneous and non-homogeneous
backward semi-Markov reward processes will be presented, as far as the
authors know, for the first time in the continuous time continuous
state non-homogeneous case.
In the continuous time semi-Markov process environment, the
distribution function that rules the transitions between the states of
the studied system can be of any type and not only exponential. This
fact is an important generalization as regards the Markov environment.
The introduction of backward time makes it possible to consider the
instant in which the system entered a state, even if it entered before
the time under consideration.
Rewards permit the introduction of a financial environment into the model.
Considering all these properties any stochastic cash flow can, in the
authors' opinion, be naturally modeled by means of semi-Markov reward
processes. Furthermore, the backward case offers the possibility of
considering the duration of an event that began before the time in
which the system is observed, and this fact can be very useful in the
evaluation of some insurance contracts.