Location of Repository

The disorder problem for compound Poisson processes with exponential jumps

By Pavel V. Gapeev

Abstract

The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of “disorder” when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jumps. The method of proof is based on reducing the Bayesian problem to an integro-differential free-boundary problem where, in some cases, the smooth-fit principle breaks down and is replaced by the principle of continuous fit

Topics: HA Statistics
Publisher: Institute of Mathematical Statistics
Year: 2005
DOI identifier: 10.1214/105051604000000981
OAI identifier: oai:eprints.lse.ac.uk:3219
Provided by: LSE Research Online

Suggested articles

Preview

Citations

  1. (1985). a n dF RISTEDT, B.
  2. (1976). A note on the Poisson disorder problem.
  3. (1994). Change-Point Problems. doi
  4. (1999). Essentials of Stochastic Finance. World Scientific, Singapore. doi
  5. (1999). Lévy Processes and Infinitely Divisible Distributions. doi
  6. (1987). Limit Theorems for Stochastic Processes. doi
  7. (1995). Normal inverse Gaussian processes and the modelling of stock returns.
  8. Onoptimum methods inquickest detectionproblems. Theory Probab.
  9. (1999). Optimal stopping for a diffusion with jumps. doi
  10. (1978). Optimal Stopping Rules. doi
  11. (1990). P ROKHOROV,Y U.V .a n dS
  12. (2002). Solving the Poisson disorder problem. doi
  13. (1965). Some exact formulas in a “disorder” problem. Theory Probab. doi
  14. (1971). The “disorder” problem for a Poisson process. Theory Probab. doi
  15. (1961). The detection of spontaneous effects.
  16. (1963). The optimum choice of the instant for stopping a Markov process.
  17. (1961). The problem of the most rapid detection of a disturbance in a stationary process.
  18. (1967). Two problems of sequential analysis. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.