There were plenty of ways for a rich Roman to spend money on fripperies, but for one interesting and very-well attested example, allow me to introduce you to a fascinating little fellow named Mullus Barbatus. Although you could be pardoned for guessing I'm talking about a Roman guy with that name, Mullus is in fact a fish and specifically a fish on which rich Romans would spend extreme amounts of money.

The red (or bearded) mullet does not typically grow larger than around 2 lb, but around the 1st Century AD a sort of fad or craze developed around very large specimens. We're told that Mullus is very fragile and responds poorly to captivity, and it was apparently a sort of hobby for rich Romans to raise them very carefully so that they would grow to large sizes (Cicero made fun of them for the time they spent on this). When the time came to eat it, the fish would be brought to the table alive in a glass jar or bowl, because it underwent a truly startling set of color changes when it was killed for the edification of the dinner guests.

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In the very struggle of its failing breath of life, first a red, then a pale tint suffuses it, and its scales change hue, and between life and death there is a gradation of colour into subtle shades....See how the red becomes inflamed, more brilliant than any vermilion! Look at the veins which pulse along its sides! Look! You would think its belly were actual blood! What a bright kind of blue gleamed right under its brow! Now it is stretching out and going pale and is settling into a uniform hue. - Seneca, Natural Questions, III.18.1,4

In addition to its dual purpose as both dinner and a show, high praise was lavished on the characteristics of the fish as food. The second-century physician Galen thought it was all rather silly, because in his opinion, a very large mullet actually tasted worse than a small one in various ways while simultaneously being much more difficult to cook. The way so many Roman writers satirized, mocked, and criticized people for their obsession with the mullet (Cicero, Juvenal, Martial, Horace, Macrobius, Tertullian, and others) suggests the real reason high prices were paid for large fish: it was an ostentatious display of wealth, and rich Romans might try to outbid one another for a particularly chonky fish just to put a thumb in their neighbor's eye.

Just how much did they pay? Many of the sources that give us actual numbers (instead of just bemoaning the expense in general terms) are satirical, and Roman writers were prone to exaggeration for literary effect in any case, so it's a bit hard to say. Seneca tells us of a four-and-a-half-pound mullet being sold in the fish market for 5,000 sesterces, and this at a time when a regular soldier was paid 3.3 sesterces a day and a slave might go for between one and three thousand. Martial makes this comparison explicit, describing (satirically) somebody selling a slave for 1200 sesterces so he could buy a four-pound mullet with the money. Suetonius tells us Emperor Tiberius was so exercised by hearing that three fish had been sold for the staggering sum of thirty thousand that he proposed the imposition of price controls on the fish markets.

Now, Suetonius doesn't vouch for whether this rumor was true and, as we have seen, extravagant fish purchases were the subject of satire and mockery and might well have been exaggerated by the time the Emperor got wind of them. But all good satire is based on some kernel of truth, and we have plenty of sources to tell us that if a rich Roman really wanted to show his contemporaries just how rich he was, he would often turn to Mullus Barbatus.