Jump Processes and Special Problems

Choosing an appropriate stochastic process to represent the evolution of a series or a stochastic environment is to date an unresolved issue. In many cases, Markov chains or processes are chosen because of their attractive analytical and tractable properties. For many situations, it is difficult to justify the use of such processes. The choice of a process should stem from both a belief and the understanding of the process evolution. The biblical adage stating that “ wise is who can foretell the unfolding of events ” is particularly relevant in this case. Wisdom and mythical knowledge aside, a stochastic process should reflect both subjective and objective information available and should not make unwarranted assumptions as to information which is not available. As a result, constructing a stochastic process requires that we: