* Nikkei up 1.7 pct, tops 75-day average
* Investors slowly share optimism on euro zone
* Shippers jump nearly 10 pct on buyback
* Olympus falls after 3rd-party panel report
TOKYO, Dec 7 (Reuters) - The Nikkei average hit a four-week high on Wednesday as investors warmed to the view that European policy-makers will come up with convincing steps this week to help resolve the region's debt crisis.
Cyclical shares such as shippers and steelmakers were also helped in making huge gains after recent credit easing by big emerging economies such as China and Brazil eased worries about a sharp slowdown in the global economy.
"Optimism is growing on the euro zone. Policy-makers have been making progress recently and the market thinks the European Central Bank and euro-zone countries will work together on the crisis," said Hideyuki Ishiguro, assistant manager of investment strategy at Okasan Securities.
The benchmark Nikkei added 1.7 percent to 8,722.17, its highest close in four weeks and ending above its 75-day moving average for the first time since late October. Last time it topped the average it managed to maintain that position for less than two days.
The broader Topix index gained 1.6 percent to 749.63.
Many market players expect the European Central Bank to cut rates on Thursday and European leaders to move towards tighter integration of the euro zone's fiscal policy at their summit meeting on Friday.
Sharp falls in euro-zone government bond yields this week, which came despite a warning from Standard and Poor's of a mass downgrade of credit ratings in the currency bloc, is also fuelling optimism over Europe.
"Banks can now buy bonds again after Merkel's Germany backed down on the European Stability Mechanism," said Eiji Kinouchi, chief technical strategist at Daiwa Securities, referring to the fact that German Chancellor Angela Merkel gave ground on a stance that investors would suffer a loss in any future bailout scheme when she met French President Nicholas Sarkozy on Monday.
Kinouchi also said banks' selling of euro-zone government bonds, which lie at the heart of the debt problem, should subside after they submit plans to enhance their capital at the year-end.
Volume picked up, with 1.81 billion shares changing hands on the main board, about 16 percent above its average for the past 20 days. Advancers outnumbered decliners by 1,366 to 204.
OLYMPUS DROPS AFTER PANEL REPORT
Shares of Olympus Corp fell 5.2 percent to 1,128 yen as short-term buyers exited positions after an independent panel investigating the accounting scandal at the firm urged it to pursue legal action against former executives responsible for the loss-hiding schemes and replace the board.
"They have been rallying on hopes on the panel report. So it was a good time to take money off the table," said a fund manager at a Japanese asset management firm.
Investors are now focusing on whether Olympus can meet a Dec. 14 deadline to report its second-quarter results and reveal the size of the restatement required to iron out its accounts.
Shipping firm Mitsui OSK Lines surged 11.2 percent to 288 yen after announcing it would form a joint supertanker service with Danish and Singapore tankers to better compete in a difficult freight market.
That also boosted rival Nippon Yusen KK by 7.9 percent to 192 yen and Kawasaki Kisen by 7.3 percent to 147 yen.
The Tokyo Stock Exchange's shippers subindex rose 9.3 percent, though that came only after shares of all three shipping firms had tumbled on Monday following reports that the companies planned to scrap 10 percent of their supertankers.
Steelmakers rose 3.6 percent as investors bought back the battered sector after China eased its monetary policy last week. (Additional reporting by Mari Saito and Lisa Twaronite; Editing by Chris Gallagher and Michael Watson)