Raised in Sheepshead Bay, Brooklyn, the child of immigrants from Albania and Croatia, Mr. Shkreli hit Wall Street at the age of 17.

While attending Baruch College, Mr. Shkreli started working as a clerk at a hedge fund, Cramer, Berkowitz & Company, in 2000. (Jim Cramer, the hedge fund manager and host of CNBC’s “Mad Money,” retired from his namesake firm that same year.) At one point, Mr. Shkreli recommended the fund short the stock of a biotechnology company, according to an interview last year with Bloomberg Businessweek. The stock fell and the hedge fund made money, prompting an inquiry from regulators about the fund’s well-timed bet. Regulators ultimately found no wrongdoing.

Mr. Shkreli set off to start his own hedge fund, Elea Capital Management, in about 2006, but it soon ran into trouble. In July 2007, Elea, Mr. Shkreli and others were sued by Wall Street investment bank Lehman Brothers for failing to pay for a put option, essentially a bet that the market would fall. When the stock market instead climbed, the fund didn’t pay. A judge issued a $2.3 million default judgment against Mr. Shkreli and the fund.

Still, the hiccup did not slow Mr. Shkreli down. He soon started a new hedge fund, MSMB Capital Management, using his initials and those of his business partner, Marek Biestek. At MSMB, a fund focused on health care, Mr. Shkreli once again plied his trade in short-selling. But rather than simply sell short a company’s shares and hope that eventually the stock would fall, Mr. Shkreli actively campaigned to make things difficult for the drug companies.

In 2011, Mr. Shkreli decided to enter the pharmaceutical industry, raising money from MSMB investors to start Retrophin.

The company looked for older, somewhat obscure drugs that it could acquire and turn into so-called specialty drugs for rare diseases, with substantially higher prices. Retrophin now sells three drugs, and total sales reached $24.1 million in the second quarter of this year.

A former portfolio manager at MSMB who was asked by Mr. Shkreli to focus on investment opportunities for Retrophin said in an affidavit early last year that he and his family were repeatedly harassed on social media by Mr. Shkreli in 2013. The emails and texts were published on Tuesday by the website Gawker.