TY - JOUR
T1 - Itô and Stratonovich integrals on compound renewal processes
T2 - the normal/Poisson case
AU - Germano, Guido
AU - Politi, Mauro
AU - Scalas, Enrico
AU - Schilling, René L.
PY - 2010/6
Y1 - 2010/6
N2 - 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 continuous-time 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.
AB - 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 continuous-time 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.
KW - Continuous-time random walk
KW - Econophysics
KW - Monte Carlo
KW - Probabilistic model
KW - Probabilistic simulation
KW - Stochastic integrals
KW - Stochastic jump process
KW - Stochastic model
KW - Stochastic theory
UR - http://www.scopus.com/inward/record.url?scp=72049092370&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2009.06.010
DO - 10.1016/j.cnsns.2009.06.010
M3 - Article
SN - 1007-5704
VL - 15
SP - 1583
EP - 1588
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 6
ER -