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19、standliquidreserves,andthecompoundPoissonriskmodelwithdoubleliquidreserves.InthecompoundPoissonriskmodelwithdebitinterestandliquidre-serves,weassumethatthecompanycanborrowasumofmoneywhichequalthedecitwhenthesurplusfallbelowzerowhileandbeginreturningthedebitcon-tinuou
20、sly,andobtaintheinterestwiththeinterestforcer>0whenthesurplusabovethesurpluslevel0(whichcalledtheliquidlevel).InthecompoundPoissonriskmodelwithdoubleliquidreserves,weassumethatthecompanycanobtaintheinterestwiththelargerinterestforcer1>0whenthesurplusbe
21、tween10and20(012),andobtaintheinterestwiththesmallerinter-estforcer2>0(themissingpartisusedtodividends)whenthesurplusabovethesurpluslevel2.Theexpecteddiscountedpenalty(Gerber-Shiu)function,whichisaveryimportantfunctionininsurancemathematics,containsthe
22、surplusbeforeruin,thedecitatruin,the