简介:Ithasbeenevidentthatthetheoryandmethodsofdynamicderivativesareplayinganincreasinglyimportantrleinhybridmodelingandcomputations.Beingconstructedonvariouskindsofhybridgrids,thatis,timescales,dynamicderivativesoffersuperioraccuracyandflexibilityinapproximatingmathematicallyimportantnat-uralprocesseswithhard-to-predictsingularities,suchastheepidemicgrowthwithun-predictablejumpsizesandoptionmarketchangeswithhighuncertainties,ascom-paredwithconventionalderivatives.Inthisarticle,weshallreviewthenovelnewconcepts,exploredelicaterelationsbetweenthemostfrequentlyusedsecond-orderdy-namicderivativesandconventionalderivatives.Weshallinvestigatenecessarycondi-tionsforguaranteeingtheconsistencybetweenthetwoderivatives.Wewillshowthatsuchaconsistencymayneverexistingeneral.Thisimpliesthatthedynamicderivativesprovideentirelydifferentnewtoolsforsensitivemodelingandapproximationsonhy-bridgrids.Rigorouserroranalysiswillbegivenviaasymptoticexpansionsforfurthermodelingandcomputationalapplications.Numericalexperimentswillalsobegiven.