* World Economic Forum annual meeting Jan. 23-27
* Little trust in elite to solve social problems - survey
* Key speeches from Italy's Monti, Germany's Merkel
By Emma Thomasson
ZURICH, Jan 21 (Reuters) - Italian premier Mario Monti will set the tone for beleaguered business and political leaders gathering in Davos this week for the annual World Economic Forum (WEF), with a speech entitled "Leading against the odds".
The pow-wow will bring together more than 1,500 business leaders and up to 50 heads of state or government, many of them, like Monti, weathered by almost perpetual crisis as they fight to bring their economies and companies through global financial turmoil and a few homegrown scandals of their own.
"It's very clear that the future of the world economy is based on restoring trust. Restoring trust in leaders, restoring trust in our future. And this means we have to move out of this crisis mode," WEF founder Klaus Schwab told a news conference.
There's still some way to go, according to a survey by global public relations firm Edelman published on Monday.
"There is an incredible lack of trust in leadership," said Richard Edelman, the firm's president and chief executive. "Levels of trust in governments are worse than for business, but they are both terrible."
Edelman's annual survey across 26 countries did show a rise in trust in business and government over the previous year, but only 26 percent trust business leaders to solve social issues and 15 percent for government leaders, and 19 percent expected business to make ethical decisions, while only 14 percent said the same for politicians.
Edelman said trust in public figures had been eroded by a string of scandals in the banking industry as well as controversies ranging from cyclist Lance Armstrong's admission of doping, to the purging of Chinese politician Bo Xilai in a murder case and a sex-abuse affair at British broadcaster BBC.
Though Europe managed - just - to keep the euro zone intact in 2012 and Washington stepped back - at the last minute - from its "fiscal cliff", a WEF survey this month showed business leaders and academics fear politicians are failing to address fundamental problems.
And they will have it all to do again in 2013, subject to the ballot box. Monti will be defending his austerity measures in parliamentary elections in four weeks, and German Chancellor Angela Merkel will be hoping a weekend defeat for her party in a regional election won't derail her re-election later this year.
A contingent from the United States including four secretaries and 14 congressmen will have another looming budget crunch at the back of their minds.
"SUDDEN SHOCKS, PROLONGED MALAISE"
The WEF's annual risk report cited inequality and the burden of government debt as the biggest economic threats and also highlighted a rise in concern about severe weather, an issue likely to be on the minds of many participants as they struggle even to reach Davos after heavy snowfall cancelled many flights.
The Algerian hostage crisis, the French campaign against Islamists in Mali and the fallout from the Arab Spring will also be hot topics, with many leaders from Africa and the Middle East attending Davos as well as several oil and gas executives.
"We face a new reality of sudden shocks and prolonged global economic malaise," Schwab said. "Future growth in this new context requires dynamism, bold vision and even bolder action."
The Davos elite will be shielded from dissent by a ring of razor wire and up to 5,000 Swiss soldiers, though activists will be handing out an award for "the worst company of the year", and Swiss left-wing groups plan small protests against financial speculation.
UBS Chairman Axel Weber and JP Morgan Chase & Co Chief Executive Jamie Dimon are among the top representatives of a chastened financial industry, which the Edelman survey shows is still the least trusted sector, on just 50 percent globally.
The WEF is trying to boost leadership skills in the tough environment, offering morning meditation and even a session with a trombonist subtitled: "How can jazz serve as a strategic model for diplomacy, leadership, collaboration and innovation?"
But chief executives are more likely to be looking for concrete deals and innovative ideas in Davos as the first signs emerge of fragile confidence returning to the world economy.
"There is more certainty than there was three or four months ago," said Kevin Kelly, chief executive of Heidrick & Struggles, a global executive search and leadership consulting firm.
"This is a turn in the mood. There is an old saying you can't fall off the floor. Economically speaking - we are in the basement now. There is no where to go but up." (Editing by Will Waterman)