Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case
✍ Scribed by Guido Germano; Mauro Politi; Enrico Scalas; René L. Schilling
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 269 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1007-5704
No coin nor oath required. For personal study only.
✦ Synopsis
Monte Carlo Econophysics a b s t r a c t
Continuous-time random walks, or compound renewal processes, are pure-jump stochastic processes with several applications in insurance, finance, economics and physics. Based on heuristic considerations, a definition is given for stochastic integrals driven by continuoustime random walks, which includes the Itô and Stratonovich cases. It is then shown how the definition can be used to compute these two stochastic integrals by means of Monte Carlo simulations. Our example is based on the normal compound Poisson process, which in the diffusive limit converges to the Wiener process.