Billionaire art and wine collector William Koch is appealing a court decision that threw out his lawsuit against Christie's in which he claimed the auction house sold him counterfeit wine.

In March 2011, Koch’s suit was thrown out by a judge who ruled for Christie's on the premise that Koch knew the bottle of 1870 Lafite wine he bought for $4,200 was counterfeit before he made the purchase.

But the dispute stretches back to purchases made decades ago...