Elon Musk's $1tn pay deal approved by Tesla shareholders Tesla shareholders have approved a record-breaking pay package for boss Elon Musk that could be worth nearly $1tn (£760bn). The unprecedented deal was approved by 75% of Tesla shareholders who cast votes at the firm's annual general meeting on Thursday. The deal requires Musk, who is already the world's richest man, to drastically raise the electric car firm's market value over a period of years. If he meets various targets, he will be rewarded with hundreds of millions of new shares. The scale of the deal is controversial, but the Tesla board argued that Musk might leave the company if it was not approved - and that it could not afford to lose him.

It's not clear that everyone is singing from the same hymn sheet though, meaning the AGM in Austin, Texas is set to become a referendum on Musk himself, after a rightward political turn which has made him one of the most polarising chief executives in recent memory. Musk himself has taken to X - which he owns - to raise the stakes higher still, saying the fate of Tesla could affect the future of civilization. He's also used his social media megaphone to amplify some of the deal's high-profile backers, including Dell Technologies' Michael Dell, Ark Invest CEO Cathie Wood, and his brother, Kimbal, who sits on the Tesla board. There is no one remotely close to my brother, Kimbal said, extolling his sibling's leadership qualities.

Is the US eyeing its next Latin American target? Why is Trump tearing down parts of the White House? Nvidia has become the first company to reach $5 trillion in market value amid a global artificial intelligence arms race. The chipmaker surge on Wednesday came only three months after the company topped the $4 trillion mark . Since the launch of ChatGPT in 2022, Nvidia's shares have climbed 12-fold as the AI frenzy propelled the S&P 500 to record highs, igniting a debate on whether frothy tech valuations could lead to the next big bubble.

Nvidia has hit a new milestone, becoming the first company in the world to reach a market value of $5tn (£3.8tn). The US chip-maker has rapidly climbed from a niche graphics-chip manufacturer to an AI titan, as euphoria about the potential of artificial intelligence keeps driving demand for its chips and propelling its stock to record highs. The company reached a market value of $1tn for the first time in June 2023 and hit the $4tn valuation mark just three months ago . Shares in the chip-maker rose as much as 5.6% to more than $212 on Wednesday morning, boosted by investor optimism about Nvidia's sales in China, which has been a geopolitical flashpoint. The world's most valuable company - the biggest winner in the AI spending spree - has soared past its rivals in the technology sector.

A prospective buyer tries the iPhone 17 Pro in Jakarta, Indonesia, on 17 October. A prospective buyer tries the iPhone 17 Pro in Jakarta, Indonesia, on 17 October. Tech company's stock enters positive territory for first time this year after gaining about 13% since new iPhone launches Apple topped $4tn in market value for the first time on Tuesday, the third tech company to hit the milestone, as robust demand for its latest iPhones allayed fears over its slow progress in the AI race. Microsoft reached a $4tn market cap for the second time the same day as the wider US stock market hit record highs. Apple's shares have gained about 13% since the new launches on 9 September, in a remarkable turnaround that pushed the stock into positive territory for the first time this year.

Non-fungible tokens (NFTs) have become a significant digital asset class, each uniquely representing virtual entities such as artworks. These tokens are stored in collections within smart contracts and are actively traded across platforms on Ethereum, Bitcoin, and Solana blockchains. The value of NFTs is closely tied to their distinctive characteristics that define rarity, leading to a growing interest in quantifying rarity within both industry and academia. While there are existing rarity meters for assessing NFT rarity, comparing them can be challenging without direct access to the underlying collection data. The Rating over all Rarities (ROAR) benchmark addresses this challenge by providing a standardized framework for evaluating NFT rarity. This paper explores a dimension reduction approach to rarity design, introducing new performance measures and meters, and evaluates them using the ROAR benchmark. Our contributions to the rarity meter design issue include developing an optimal rarity meter design using non-metric weighted multidimensional scaling, introducing Dissimilarity in Trades (DIT) as a performance measure inspired by dimension reduction techniques, and unveiling the non-interpretable rarity meter DIT, which demonstrates superior performance compared to existing methods.

Microsoft is now the second company ever to surpass 4 trillion in market valuation, following artificial intelligence giant Nvidia. Microsoft, which is traded under the ticker "MSFT", is continuing to surge and as of noon in New York City (16:00 GMT) on Thursday, it is up 4.6 percent from the market open. The technology behemoth said it will spend 30bn in capital spending for the first quarter of the current fiscal year to meet soaring artificial intelligence (AI) demand. Microsoft also reported booming sales in its Azure cloud computing business on Wednesday. "It is in the process of becoming more of a cloud infrastructure business and a leader in enterprise AI, doing so very profitably and cash generatively despite the heavy AI capital expenditures," said Gerrit Smit, lead portfolio manager, Stonehage Fleming Global Best Ideas Equity Fund. Redmond, Washington-headquartered Microsoft first cracked the 1 trillion mark in April 2019.

Nvidia has notched a market capitalisation of 4 trillion, making it the first public company in the world to reach the milestone and solidifying its position as one of Wall Street's most-favoured stocks. On Wednesday, shares of the leading chip designer rose as much as 2.5 percent to an all-time high of 164, benefiting from the continuing surge in demand for artificial intelligence technologies. The stock's recent rally comes despite a sluggish start to the year, when the emergence of a Chinese discount artificial intelligence model developed by DeepSeek shook confidence in stocks linked to the sector. Nvidia achieved a 1 trillion market value for the first time in June 2023 and tripled it in about a year, faster than Apple and Microsoft, the only other United States firms with a market value of more than 3 trillion. Microsoft is the second-biggest US company, with a market capitalisation of 3.75 trillion.

Chipmaker Nvidia became the first public company in history to scale a 4tn market value on Wednesday as its stock price continues a years-long stratospheric rise. Shares of the top chip designer rose roughly 2.4% to 164, benefiting from the ongoing surge in demand for artificial intelligence technologies. Nvidia's chips and associated software are considered world leaders for building artificial intelligence products. Nvidia achieved a 1tn market value for the first time back in June 2023 and the surge continued unabated with its market value – the total value of its shares – more than tripling in about a year, faster than Apple and Microsoft, the only other US firms with a market value of more than 3tn. Apple was the first company to reach a valuation of 3tn, back in 2022.

We study a contextual version of the repeated brokerage problem. In each interaction, two traders with private valuations for an item seek to buy or sell based on the learner's-a broker-proposed price, which is informed by some contextual information. The broker's goal is to maximize the traders' net utility-also known as the gain from trade-by minimizing regret compared to an oracle with perfect knowledge of traders' valuation distributions. We assume that traders' valuations are zero-mean perturbations of the unknown item's current market value-which can change arbitrarily from one interaction to the next-and that similar contexts will correspond to similar market prices. We analyze two feedback settings: full-feedback, where after each interaction the traders' valuations are revealed to the broker, and limited-feedback, where only transaction attempts are revealed. For both feedback types, we propose algorithms achieving tight regret bounds. We further strengthen our performance guarantees by providing a tight 1/2-approximation result showing that the oracle that knows the traders' valuation distributions achieves at least 1/2 of the gain from trade of the omniscient oracle that knows in advance the actual realized traders' valuations.