So far the prince is moving cautiously. He is seeking a listing only on Riyadh’s Tadawul stock exchange. A foreign listing in a more complex and risky environment like New York or London has been deferred, and some analysts are skeptical about it ever happening.

The prince could even back away from the stock offering if circumstances change or it fails to sufficiently excite investors. The company has six months to list shares, under the approval granted Sunday by the Saudi Capital Markets Authority.

In recent weeks analysts have privately estimated that the sale would deliver a lower valuation than the $2 trillion goal the prince set more than three years ago. Now they are beginning to state those figures publicly.

Analysts at Bernstein, an investment firm, estimated that Aramco’s “fair value” was between $1.2 trillion and $1.5 trillion. In a note to clients on Monday, the analysts said they had based the estimate on metrics like dividends and earnings forecasts.

A person familiar with the offering , speaking on the condition of anonymity to discuss private conversations, said there were signs the prince was edging toward accepting a valuation around $1.8 trillion. A prospectus with more details is expected to be released soon.