This is going to be a very broad generalization, sorry I can't give any more specific info at the moment. Also this is more on the early empire as i'm not really sure in regards to the later empire. Roman Emperors (or their family) weren't seen to "own" the empire the same way medieval monarchs did. A Roman Emperor was the guy who simply ran the empire, although this title of office was hereditary(but not always). The Emperor simply owned the lands and property from his family. These were given to them by their Fathers, the emperors (biological or adopted). When the previous emperor died they would give out their estates to their family in their will. The Office of Emperor was just another thing that they more or less owned and they bequeathed it to the person/son they thought would do the best job. Even though they owned the office they didn't own all of the property of the State.
I can't give you specific numbers, but I can tell you that when Augustus had conquered Egypt he was rich enough to pretty much personally underwrite the financing of every change he made to the empire (of which there were many).
I can also highlight a few specific sections of his Res Gestae Divi Augusti (roughly 'the deeds of the divine revered one'). Whilst one of the earliest examples of PR, the figures might be able to give you some kind of an idea of how much Augustus, the first emperor, was worth.
15 I paid to the Roman plebs, HS 300 per man from my father's will and in my own name gave HS 400 from the spoils of war when I was consul for the fifth time (29 B.C.E.); furthermore I again paid out a public gift of HS 400 per man, in my tenth consulate (24 B.C.E.), from my own patrimony; and, when consul for the eleventh time (23 B.C.E.), twelve doles of grain personally bought were measured out; and in my twelfth year of tribunician power (12-11 B.C.E.) I gave HS 400 per man for the third time. And these public gifts of mine never reached fewer than 250,000 men. In my eighteenth year of tribunician power, as consul for the twelfth time (5 B.C.E.), I gave to 320,000 plebs of the city HS 240 per man. And, when consul the fifth time (29 B.C.E.), I gave from my war-spoils to colonies of my soldiers each HS 1000 per man; about 120,000 men i the colonies received this triumphal public gift. Consul for the thirteenth time (2 B.C.E.), I gave HS 240 to the plebs who then received the public grain; they were a few more than 200,000.
16 I paid the towns money for the fields which I had assigned to soldiers in my fourth consulate (30 B.C.E.) and then when Marcus Crassus and Gnaeus Lentulus Augur were consuls (14 B.C.E.); the sum was about HS 600,000,000 which I paid out for Italian estates, and about HS 260,000,000 which I paid for provincial fields. I was first and alone who did this among all who founded military colonies in Italy or the provinces according to the memory of my age. And afterwards, when Tiberius Nero and Gnaeus Piso were consuls (7 B.C.E.), and likewise when Gaius Antistius and Decius Laelius were consuls (6 B.C.E.), and when Gaius Calvisius and Lucius Passienus were consuls (4 B.C.E.), and when Lucius Lentulus and Marcus Messalla were consuls (3 B.C.E.), and when Lucius Caninius and Quintus Fabricius were consuls (2 B.C.E.) , I paid out rewards in cash to the soldiers whom I had led into their towns when their service was completed, and in this venture I spent about HS 400,000,000.
17 Four times I helped the senatorial treasury with my money, so that I offered HS 150,000,000 to those who were in charge of the treasury. And when Marcus Lepidus and Luciu Arruntius were consuls (6 A.C.E.), I offered HS 170,000,000 from my patrimony to the military treasury, which was founded by my advice and from which rewards were given to soldiers who had served twenty or more times.
18 From that year when Gnaeus and Publius Lentulus were consuls (18 Bc), when the taxes fell short, I gave out contributions of grain and money from my granary and patrimony, sometimes to 100,000 men, sometimes to many more.
Written after Augustus' death:
1 All the expenditures which he gave either into the treasury or to the Roman plebs or to discharged soldiers: HS 2,400,000,000.
http://classics.mit.edu/Augustus/deeds.html Here's the link for the translation of the Res Gestae I used.