What's a global bank with a $1 trillion balance sheet to do?

Citigroup faces a frightening next few weeks. With recessions around the world threatening to create a new wave of consumer-driven losses for the bank, this week's cost-cut plan, a focused strategy, and an endorsement from one of the biggest and most influential shareholders are simply not going to cut it. Shares of Citigroup are down 50 percent this week alone, and there are no obvious solutions.

David Enrich of the Wall Street Journal reports that Citi has now begun weighing whether to sell off pieces of the company or even the company itself.

He cautions that these internal discussions are very preliminary and that the chief executive, Vikram Pandit, and the board, remain committed to the bank's strategy of cutting costs and streamlining to weather the financial storm.

Erich Dash and Louise Story of the New York Times pour some cold water on these discussions, saying that "Citigroup executives are seeking to stabilize the stock price, but at this point they are not actively exploring selling or splitting up the company."

And they note there are few buyers willing to pay the prices Citi would seek for its assets.

Yves Smith on the Naked Capitalism blog goes further, pointing out that American International Group, the insurer that had to be rescued by the government, had more desirable assets than Citi and could not find buyers.

"Financial institutions are too capital starved to be sticking their necks out now, and private equity firms cannot meet their target returns without leverage, which they cannot get right now. And who, pray tell, would buy the entire bank?"

So what are the possibilities for Citi?

More Government Help. The bank has raised $50 billion in new capital on its own and is getting $25 billion as part of the $125 billion injected into the nation's nine biggest banks under TARP. Hits from credit cards, commercial real estate, and consumer lending may produce another $20 billion in losses for 2009. Will the government need to come up with another $25 billion for Citi?

Attract a Big Investor. On Thursday, Prince Alwaleed bin Talal of Saudi Arabia said that he would increase his stake in Citi to 5 percent from less than 4 percent, expressing his support for Pandit and the bank's management. Yet, the shares still fell 26 percent. The market was unimpressed with the prince because his move represented a relatively small amount of money—he was arguably just retopping an investment that had been diluted by Citi's capital raises. And the prince's reputation as a savvy investor has been questioned by his loyalty to the bank. But if someone like a Warren Buffett or another financial institution were to take a 5 percent stake, proclaiming Citi's long-term viability, that would change the perception of the bank quickly.

Stay the Course. Just get through to 2009. This is not entirely wishful thinking. Pandit's moves do make strategic sense, and there is a real likelihood that the fear that has buffeted markets and Citi will ease with a new year and a new government. Richard Beales on Breakingviews.com says of Citi:

"There are recovery scenarios, but precious few investors have the nerve to bet on them. It's all about safe, relatively predictable investments that won't lose any more money. That may, perhaps, be a particularly acute feeling as an exhausting 2008 winds down—the end of the reporting year for most market players."

We may learn more today as Pandit plans to hold a meeting for senior managers and the board of Citi will meet, according to reports.