The pilot stated that he was attempting to taxi from the ramp area when the accident occurred. He reported that the airplane taxi lights were on; however, the edge of the ramp was not marked and before he could complete a turn, the nose wheel departed the pavement. He noted that the grass area between the ramp and parallel taxiway appeared to be level and suitable for crossing. After assessing the situation, he attempted to taxi across the grass area to the parallel taxiway about 50 feet from the ramp. However, the airplane encountered a drainage ditch located between the ramp and the taxiway, which caused substantial damage to the delta fins on the underside of the aft fuselage. The pilot noted that there were no mechanical failures or malfunctions associated with the airplane prior to the accident. He commented that the ramp was poorly illuminated and the high overcast clouds combined to create "very dark" lighting conditions.