The New York company's shares have declined since its debut earlier this month at $36 a share. It had priced its initial public offering at $39 a share.
Oscar Health shares at last check were 2.2% lower at $25.15.
The company gets the majority of its revenue from selling insurance plans in the marketplace that was set up by the Affordable Care Act.
Analysts at Goldman Sachs initiated coverage with a buy rating and price target of $44. The investment firm said Oscar Health is an opportunity to buy into a differentiated offering "levered to attractive secular themes."
"While, broadly, we think competition poses a risk, OSCR has demonstrated an ability to grow through increasing competition, which we think will continue near term," analyst Robert Jones said.
Credit Suisse initiated coverage with an outperform rating and $34 price target.
"The main growth drivers for Oscar Health over the next 10 years are: (1) acquiring members in existing markets, (2) launching new markets and states, (3) introducing new products/plans, (4) creating new partnerships and potential acquisitions, and (5) monetizing the technology," analyst Jailendra Singh said.
Cowen initiated coverage of Oscar Health with a market-perform rating and $29 price target.
"We like OSCR's exposure to higher-margin end markets, strong growth profile, and growth potential in the platform business; the latter of which we think could be a potentially significant long-term profit driver," analyst Charles Rhyee said..
However, we are cautious on OSCR's reliance on the individual exchange market given rising competition."