Thispaperinvestigatesthepricingofoptionswrittenonnon-tradedassetsandtradingstrategiesforthestockandoptioninanexponentialutilitymaximizationframework.Undertheassumptionthattheoptioncanbecontinuouslytradedwithoutfrictionjustasthestock,adynamicrelationshipbetweentheiroptimalpositionsisderivedbyusingthestochasticdynamicprogrammingtechniques.Thedynamicoptionpricingequationsarealsoestablished.Inparticular,thepropertiesoftheassociatedsolutionsarediscussedandtheirexplicitrepresentationsaredemonstratedviatheFeynman-Kacformula.Thispaperfurthercomparesthedynamicoptionpricetotheexistingpricenotions,suchasthemarginalpriceandindifferenceprice.
