European shares edged higher on Tuesday, extending ‌the previous session’s rally, sparked by a preliminary agreement between the US and Iran that could end their war and allow a resumption of ​oil flows through the Strait of Hormuz.The pan-European Stoxx 600 index ended 0.3 per cent higher, after closing at a record high on Monday. Oil prices declined for the fourth ​consecutive session, in a positive development for the oil-import-dependent Continent, with Brent Crude trading near $82 (€70.62) a barrel, easing some concerns over inflation that had pushed expectations ⁠of further monetary tightening.DUBLINThe Iseq All-Share Index advanced for a fourth straight session to gain 1.1 per cent and close at a fresh record high of 13,683.32. Banking stocks were in demand, with AIB rising 1.5 per cent to almost €10.40, while Bank of Ireland pushed 2.4 per cent higher to €17.82. Oil-sensitive travel stocks were also a bright feature as fuel prices continued to fall. Ryanair edged 0.8 per cent higher to €26.04, while Irish Ferries parent Irish Continental Group (ICG) rose 0.9 per cent to €6.38. Kingspan jumped 2.8 per cent to €86.85 amid speculation that the outlook for the global economy has improved. LONDONThe FTSE 100 made strong progress, rising 0.6 per cent, as oil fell further amid growing confidence in the US-Iran peace process.Improved confidence about economic prospects lifted banks NatWest, HSBC and Barclays by 2.2 per cent, 1.8 per cent and 1.5 per cent respectively.Housebuilders also rallied, with Barratt Redrow up 1.8 per cent and Persimmon up 2.5 per cent.Rolls-Royce added a further 2.6 per cent after its Swedish small nuclear reactor contract win on Monday.On the FTSE 250, Currys jumped 4.2 per cent as RBC Capital Markets upgraded to outperform – the equivalent of a buy recommendation. Wealth manager Rathbones’s shares slumped 16.8 per cent as it paused taking on certain higher-risk clients in the wake of a review prompted by engagement with the UK financial conduct watchdog. The company outlined the moves after a skilled person review, which followed engagement with the UK Financial Conduct Authority.EUROPESectors that are ⁠expected to fare better during times of economic ​certainty did well in Europe on Tuesday. Industrial goods and ​services advanced 1.1 per cent, while banks led broader gains with a 1.7 per cent jump.Among corporate updates, UniCredit gained 4.2 per cent after Germany rejected the Italian lender’s offer to buy Commerzbank shares.Concerns also resurfaced that tech companies were increasingly relying on debt funding, which has sparked sell-offs globally several times since last year.STMicroelectronics fell 4.1 per cent per cent after announcing plans to issue convertible bonds worth $1.5 billion. NEW YORKWall Street stock indices were mixed in early afternoon trading – with the S&P 500 and Dow Jones Industrial Average ahead and the Nasdaq lower – as oil prices continued to fall, while SpaceX surpassed Amazon’s market value during the morning to become the fifth-most-valuable US firm. The Elon Musk-led company said it would acquire software firm Anysphere for $60 billion in a bid to ramp up its presence in the enterprise AI market.Memory chip stocks rose, with Western Digital and Seagate Technology advancing. Financial shares benefited as investors rotated into economically sensitive pockets of the market. Goldman Sachs, JPMorgan and Bank of America stood out as strong spots. The energy index lost 0.4 per cent ‌as ​oil prices dropped to nearly a three-month low.Markets will next turn to ​the US Federal Reserve’s monetary policy decision on Wednesday. The central bank is widely expected to hold interest rates at the 3.50 to 3.75 per cent range, with investors closely watching Fed chair Kevin Warsh’s ‌comments on inflation, unemployment and the economic outlook.Qualcomm rose after The Information reported that ‌the chipmaker was in talks to acquire AI chip start-up Tenstorrent for $8 billion to $10 billion.Robinhood was up as the trading platform said it would cut 10 per cent of its ​full-time workforce and close remaining open roles.– Additional reporting, Reuters, Press Association