He also said the board never approved consulting agreements used to pay MSMB investors in Retrophin stock.
Aselage testified that Shkreli contacted him "out of the blue" in 2012 and said he wanted Aselage to join his new company, Retrophin.
In a later call, Aselage said, Shkreli talked about his vision for "a great, new pharmaceutical company" and claimed that he was a "very successful investment manager."
However, prosecutors have claimed, Shkreli had already failed at running one hedge fund, Elea Capital, and had lost much if not all of the investor money he was handling at the MSMB funds.
Aselage said he agreed to join Retrophin as CEO. During his tenure in that post, he testified, he found Shkreli to be "bright" and capable of "knocking down walls."
But Aselage also came to feel Shkreli was really the one in charge of the company, while using Aselage as the face of the firm.
Aselage said that shortly after starting his job he found out the Retrophin did not have funding for operations, contrary to what Shkreli had told him.
At one point, Aselage said, Retrophin was "running on fumes."
He also testified that there was a concern about commingling of finances between the MSMB funds and Retrophin, and that it sometimes wasn't clear which employees were working for which firm.
Aselage later found out that Retrophin did not have insurance for its directors and officers to protect them personally if they were sued in connection with company activities.
"It's America," Aselage said. "In America, you can sue everybody ... it can wipe out someone's life savings."
Aselage said the lack of insurance, and the questions about who was actually in charge of Retrophin, left him in an "untenable position."
He testified that he wanted to resign as both CEO and a member of the company's board of directors.
But Shkreli and another Retrophin official convinced him to remain on the board.
On Wednesday, the former chairman of the board of Retrophin, Steven Richardson, testified about the events that led the board to fire Shkreli in 2014 and to re-install Aselage as CEO.
Richardson said that instead of curbing stock trading by Retrophin employees in what was an effective hedge fund within the company, Shkreli set up a commission-incentive structure for those workers, and then lied about it to Richardson.
Richardson also testified that Shkreli had himself been trading in Retrophin stock during periods when he was barred from doing so, and also was giving some new employees company shares without keeping track of the amounts. That latter practice risked diluting the value of shares held by existing Retrophin investors.
On Tuesday, Richardson testified that Shkreli had made him uncomfortable by musing about having sex with a male worker at his hedge fund's office, or with a male waiter.
Richardson, who is gay and who was an investor in Shkreli's fund, said he believed Shkreli was saying such things because he believed Richardson wanted to hear them.