The inauguration of Donald Trump as the President of the United States has sent ripples through global financial markets, with European shares displaying cautious advances, amidst a backdrop of growing investor anxiety. As of 0952 GMT, the pan-European STOXX 600 index inched up by 0.1%, reaching a near three-month high buoyed by gains in banking and travel sectors, despite the closure of U.S. stock markets in observance of Martin Luther King Day, leading to lighter trading volumes globally.

The anticipated inauguration at 12:00 pm ET (1700 GMT) has captured the world's attention, as investors eagerly await the initial executive actions Trump has promised in areas such as immigration, energy, and trade tariffs. Ipek Ozkardeskaya, a senior market analyst at Swissquote Bank, expressed uncertainty over Trump's plans, suggesting a sense of unpredictability surrounds his forthcoming policies which could potentially trigger inflationary pressures both in the U.S. and Europe.

The market's optimism is tempered by apprehensions around Trump's potential protectionist trade tactics, which could reverberate through international markets, affecting key trading partners. Ozkardeskaya noted, There is the hope that Trump is coming on the scene with a first punch and he's going to soften his tone and his next four years won't look as bad. However, many remain on edge about the economic implications of his proposed policies.

Financial markets have been particularly sensitive, with the banking index observed as the biggest sectoral gain, rising by 0.7%, followed closely by the travel and leisure index at 0.4%. Conversely, the utility sector presented a downward drag, with a 1.1% drop, which tempered the overall gains in the equity markets.

In Germany, economic data revealed that producer prices rose by 0.8% in December, falling short of market expectations. This development has implications for the European Central Bank's policy decisions, as policymaker Robert Holzmann cautioned about the potential for the central bank to undermine its credibility should it decide to reduce interest rates amidst a swift rise in inflation.

Investor focus will also be on the upcoming European Central Bank meeting scheduled for January 30, where a rate cut of a quarter-point has been predicted by numerous analysts. Additionally, the World Economic Forum taking place in Davos this week is another significant event where global political, business, and finance leaders are expected to weigh in on current economic uncertainties.

In European corporate news, industrial technology firm Hexagon saw a 1.3% rise in its shares following the announcement of Anders Svensson's appointment as CEO, moving from his prior role as CEO at Konecranes, whose shares dipped by 4%. In the energy sector, Siemens Energy experienced a 2.1% decline, attributed by traders to a UBS downgrade to a sell rating. On a positive note, Belimo Holding, known for its heating and ventilation solutions, reported revenues surpassing market forecasts, with shares advancing by 2.8%.