Wall Street started the week with a big rally.

Stocks rallied on Monday as investors seized on signals that the coronavirus outbreak may be peaking in some of the world’s worst-hit places.

The number of new confirmed deaths and infections is slowing in parts of Europe, and the number of deaths in New York has been steady for two days. In Italy and Spain, the total number of patients continues to climb, but the rate of new infections is no longer rising.

Wall Street analysts have been closely tracking the growth path of infections, with some spotlighting recent news as an indication that the outbreak could be near a peak in the United States. Analysts highlighted the tentative deceleration of infections in New York as a good sign for other virus hot spots in the country, as well as for stock market sentiment.

“This does not mean that the all clear is immediate, nor does it mean that the U.S. economy will quickly recover. But the light at the end of the tunnel is starting to emerge,” Dan Clifton, a partner at Strategas Research Partners, a financial and Economic consulting firm, wrote in a note.

The optimism drove shares sharply higher. The S&P 500 rose 7 percent, its biggest gain since March 24, when it climbed more than 9 percent.

Some areas of the market that have been hit hardest by shutdowns of economic activity soared. The hotel chain Marriott and the casino company Wynn, for example, each rose more than 15 percent. Credit card companies also rallied, after being hammered by soaring unemployment in recent weeks, which makes people less likely to pay their bills. Capital One and Discover Financial both jumped more than 15 percent. Payment giant Visa rose more than 11 percent.

Shares of cruise operator Carnival jumped by more than 20 percent after Saudi Arabia’s state investment fund said it has acquired an 8 percent stake in the company.

Still, there was a strong defensive tilt to trading. The utilities sector — typically an area dominated by risk-averse investors — was one of the best performing in the S&P 500, with a gain of almost 8 percent.

That suggests investors still see plenty of reason to be cautious.

The slow of the spread of the disease is a good first step in reducing the impact on hospitals, but it still could take some time to open the economy more broadly. On Monday, Gov. Andrew M. Cuomo of New York cautioned that the state was still facing an emergency.

Plus, consumers — the chief economic engine in the United States — remain worried about how efforts to contain the virus will affect them. A Federal Reserve survey conducted in March showed that Americans’ pessimism about the labor market is testing new limits.

Expectations that unemployment will be higher a year from now rocketed up, as have workers’ estimations of the chance that they may lose their own job, according to the Federal Reserve Bank of New York’s Survey of Consumer Expectations.

A more widespread approach to testing that gives companies and consumers confidence that life is returning to some semblance of normal will be crucial, Scott Clemons, the chief investment strategist for private banking at Brown Brothers Harriman, wrote in an email.

“Progress on that front, or the lack thereof, is a potential source of future market volatility,” Mr. Clemons wrote. “I don’t think we’re out of the woods quite yet.”

The Fed will support banks that lend to small businesses.

The Federal Reserve said on Monday that it would provide a backstop to banks making loans to small businesses as part of the government’s coronavirus-tied lending program, an effort to get financing to vulnerable companies.

Congress has made loans available to small businesses as part of the $2 trillion stimulus package it passed in March. The Fed said Monday that it would establish a program giving banks an incentive to lend under the so-called Paycheck Protection Program, which is supposed to funnel some $350 billion in loans to strapped companies.

While the central bank released few particulars — saying only that additional details would be announced this week — the program could take several forms, either making outright purchases of those loans once banks have extended them, or providing funding to the banks to help them lend.

The G20 is expected to meet this week over the oil glut.

Representatives of Group of 20 countries are expected to meet “very soon — this week” to address the enormous oversupply of oil on the world markets, Fatih Birol, the executive director of the International Energy Agency, said in an interview Monday.

Mr. Birol, whose organization serves as an energy watchdog for industrialized nations, said that the glut of oil building in the market is too big for the Organization of the Petroleum Exporting Countries and other producers, including Russia, to resolve. This group, known as OPEC Plus, is expected to meet by teleconference on Thursday, in part to resolve a price war between Saudi Arabia and Russia.

Mr. Birol said that even if these oil officials agreed to reduce production by 10 million barrels a day — a staggering amount equivalent to about 10 percent of consumption in normal times — there would still be a surplus this quarter of 15 million barrels a day, according to his agency’s numbers.

Initially, “there would be an upbeat mood in the market, but after a while people would realize there is still a huge amount of supply overhang,” he said.

Mr. Birol also said that he was worried about the fate of the global oil industry, which he called “one of the pillars of the global economy,” and its tens of millions of employees.

Coronavirus ‘war bonds’ are under consideration, Kudlow says.

President Trump and his economic advisers are considering the possibility of issuing coronavirus “war bonds” as an effort to finance the swelling cost of propping up an economy facing a deep recession.

The CNBC television host Jim Cramer has been calling publicly for the Trump administration to issue such bonds to finance the economic relief effort and rally the country. On Monday, he asked Larry Kudlow, Mr. Trump’s top economic adviser, if the concept was on the table.

“You know, Jimmy, as far as I’m concerned, I think it’s a great idea,” Mr. Kudlow said. “This is a time, it seems to me, to sell bonds in order to raise money for the war effort.”

Mr. Kudlow said that he has spoken to Mr. Trump and Treasury Secretary Steven Mnuchin about the idea. They have not decided whether to move ahead with it or what the maturity or rate on the bonds would be. It’s possible that a war bond could be the existing 30-year bond, rebranded.

Earlier in Mr. Trump’s term, Mr. Mnuchin formally studied the possibility of issuing 50- or 100-year bonds but found that there was not sufficient appetite for them. In January, the Treasury Department announced plans to roll out 20-year bonds for the first time since 1986.

When asked about the idea by Mr. Cramer last week, Mr. Mnuchin suggested that the current menu of bonds was insufficient.

“You can buy as many 30-years as you want,” Mr. Mnuchin said. “That’s no problem.”

There has been discussion in Europe about the possibility of the European Union issuing “corona bonds” to help finance health systems and emergency employment measures.

Democrats tell Mnuchin to move fast on airline aid.

Senator Chuck Schumer of New York, the Democratic leader, and Speaker of the House Nancy Pelosi urged the Trump administration to quickly provide America’s airlines with direct payroll assistance.

Major airlines began submitting their applications for government support to the Treasury Department on Friday, but there was growing concern within the industry that Treasury Secretary Steven Mnuchin will demand strict terms, such as large equity stakes in the companies, to ensure that taxpayers are compensated.

The Democrats, in a letter reviewed by The New York Times on Sunday, said they feared that if Mr. Mnuchin drove too hard a bargain that airlines would balk and lay off more workers.

The Treasury had no comment on the letter from the lawmakers.

JPMorgan’s Jamie Dimon expects a ‘bad recession.’

Jamie Dimon’s annual letter to shareholders is widely read on Wall Street — he often uses it to discuss not just the bank’s performance, but regulation, the economy and America’s role in the world. In his latest letter, published today, the chief executive of JPMorgan, America’s largest bank, says he expects “a bad recession combined with some kind of financial stress similar to the global financial crisis of 2008.”

Companies have recently drawn down more than $50 billion from their credit lines with the bank, which “dramatically exceeds” the amount borrowers tapped during the last recession, Mr. Dimon wrote. Still, JPMorgan had nearly $300 billion in undrawn commitments at the end of last month, he added.

The bank has kept three-quarters of its 5,000 branches open during the pandemic. Like other banks, JPMorgan has waived some fees and extended repayment periods for mortgages, auto loans and the like. “We are exposing ourselves to billions of dollars of additional credit losses as we help both consumer and business customers through these difficult times,” Mr. Dimon wrote. The projected hit to the bank’s earnings — it made $36 billion in net profit last year — will be detailed when it reports its first-quarter financials next week.

In his letter, Mr. Dimon also added his voice to the chorus of captains of industry worried about restarting the economy, noting that a “disciplined” reopening would “minimize the time, extent and suffering caused by the economic downturn.”

With much of the country under stay-at-home orders that are keeping drivers off the roads, Allstate says it will issue partial refunds to most of its auto insurance customers, while American Family Insurance said it would issue customers one-time payments of $50 per vehicle.

The company said Monday that it would return 15 percent of customers’ premiums for April and May. The refund will be sent back to Allstate, Esurance and Encompass customers through their usual payment method or credited to their accounts. The repayments would total more than $600 million, the company said.

Tom Wilson, Allstate’s chief executive, cited “an unprecedented decline in driving” as the reason for the refunds. “This is fair because less driving means fewer accidents,” he said in a statement.

Allstate is also allowing auto- and home-insurance customers to delay two consecutive payments or choose to pay what they can afford. It is also expanding insurance coverage to people who use their personal vehicles to deliver food, medicine and other goods for commercial purposes — activities that are usually not covered by personal auto insurance policies.

Concerns, and employee voices, rise about the safety of Amazon sites.

As governments order Americans to stay home during the pandemic and homes across the country turn to Amazon for food, medicines and other supplies, many of the more than 400,000 warehouse workers who fulfill orders for the online retailer have remained on the job. The challenge lies in keeping them there.

Orders for groceries have been as much as 50 times higher inside Amazon, and the company is struggling to keep its warehouses staffed as concerns grow that these massive distribution centers have been contaminated, according to more than 30 current and former Amazon employees who spoke with The New York Times.

Last month, one person with knowledge of the situation said, worker attendance inside Amazon warehouses had dropped as much as 30 percent.

Though Amazon workers are not unionized, the situation has provided added leverage for workplace organizers inside the company to demand more pay and better sick leave. Last week, small groups of workers staged protests against working conditions inside two Amazon warehouses, and government officials in New York State and New York City said they were investigating whether the company improperly fired one employee who was part of a protest on Staten Island.

Catch up: Here’s what else is happening.

• BMW said on Monday that it was extending the suspension of production at its plant in Spartanburg, S.C., by three weeks to at least April 30.

• Boeing has extended the closing of its production operations in the Seattle area “until further notice.” The company’s work force has been hit hard by the pandemic and its business hurt by the grounding of the travel industry. Airbus, a Boeing competitor, said on Monday that it was pausing production at a facility in Mobile, Ala.

• Japan will offer an economic rescue package valued at roughly one-fifth of its annual economic output, or nearly a trillion dollars, Prime Minister Shinzo Abe said on Monday, to prevent its economy from collapsing under the strain of the coronavirus. He was also preparing to declare a state of emergency, which could bring many of the country’s businesses to a standstill.

Reporting was contributed by Karen Weise, Alan Rappeport, Ron Lieber, Kate Conger, Ben Dooley, Cade Metz, Jeanna Smialek, Stanley Reed, Niraj Chokshi, Nicole Sperling, Neal E. Boudette, Eduardo Porter, Jason Karaian, Jack Ewing, Mohammed Hadi, Katie Robertson, Carlos Tejada and Daniel Victor.