Jump Processes and Special Problems

  • Charles S. Tapiero


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:
  • * Identify the evolutionary structure of the underlying process

  • * Find an appropriate mathematical characterization that formulates such evolution and

  • * Construct the model in terms of the disposable information (usually time series). In this chapter we shall be concerned with a number of approaches and processes which depart from the basic random walk models considered earlier. Some of these models have still the Markov property such as jump processes as well as processes with absorption and reflection boundaries. Other models, such as nonlinear stochastic models are far more difficult to deal with, although they are an essential part of real phenomena. Such models are discussed in the next chapter however. As with the previous chapters, we emphasize again many applications in finance, insurance and risk.


Random Walk Poisson Process Wiener Process Price Process Jump Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Charles S. Tapiero
    • 1
  1. 1.ESSECCergy PontoiseFrance

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