LONDON -- "Never catch a falling knife," investors say, because a share that has fallen may continue to plummet. I would beg to differ; if you have the skill to buy in near the bottom -- and it is a skill -- then you might just bag yourself an absolute bargain.

This is an investing technique I have used before with some success, so I thought I'd have a search for more bargains. Here is what I found: three falling knives which I think are worth a closer look.

Resolution
A casual skim through the highest-yielding shares in the FTSE 100 (INDEX: ^FTSE) brought up a company I knew very little about: Resolution Limited (LSE: RSL.L). This is an insurance company with a rather unusual history.

The firm was started in 2008 with a strategy of buying up unloved life insurance assets and wringing out excess costs from these companies. The business bought Friends Provident in 2009, and a year later it acquired Axa Sun Life Holdings. Then, in 2011, BUPA Health Assurance was bought out.

This company has particular appeal for high-yield investors: At the current price of 213 pence, it is on a forecast yield of 9.8% -- very juicy, and one of the highest yields in the Footsie.

Why is the yield so high? Well, the company had a rough 2011, making a loss of 4.3 pence a share, having made a profit of 80 pence a share in 2010. The loss was due to a fall in value of its long-term investments (operating profit was actually up). Since these results came out, the shares have been tumbling.

But, importantly, the company was still able to raise its dividend by 10%, as it has an impressive capital surplus of 2.1 billion pounds. What's more, things are looking much better for 2012, with the firm forecast to return to profit. It is currently on a forecast P/E ratio of 9.6, which falls to 7.6 for 2013. Resolution is definitely in bargain territory now.

Has the knife hit bottom yet? Well, having seen what has happened to other companies in the out-of-favor insurance sector, such as Aviva (NSYE: AV) and Royal & Sun Alliance (LSE: RSA.L), I wouldn't be surprised to see Resolution fall in price for a while yet. So, for me, this is one to keep on the watchlist and monitor patiently.

First Group
If there are two themes coming through from this article, they are high-yield investing and the importance of patience.

I tipped First Group as a high-yield bargain back in February, but I was too quick off the mark. The shares were recently trashed upon the release of a set of poor results indicating that the company's U.K. bus operations were suffering as Britain's economy remains stuck in the doldrums.

A year ago, First Group's share price stood at 350 pence. After the profit warning, the shares slumped, and they now stand at 210 pence. This puts the company on a forward P/E ratio of 5, with a prospective dividend yield of 11%.

Will the dividend be cut? So far the board is holding firm, reiterating its commitment to raising the dividend by 7% a year, despite the profit warning. Even if the dividend is just frozen, it is reason enough to buy the share.

Yes, it is true that we now expect First Group's profits to be eroded for the next couple of years as U.K. bus margins are squeezed, but even if you factor in this bad news, in my view the shares still look too cheap. After all, the company's U.S. business and the train operation are still doing well.

I feel the shares may have now bottomed, and any piece of good news, such as a train franchise win, could give the share price a boost.

AstraZeneca
Last year I argued that of the two pharma giants AstraZeneca (NSYE: AZN) and GlaxoSmithKline, I would go for GSK, as I feared AstraZeneca was heading for a fall because of the steepness of its patent cliff.

I think AstraZeneca is now in the middle of tumbling down that patent cliff, and it is suffering just as I feared. The expiration of patents for such blockbusters as Seroquel and Symbicort, along with a weak drugs pipeline, points to difficulties ahead for AstraZeneca.

Thus, AstraZeneca is a cheap share that has been getting cheaper. A year ago the company's shares touched 3,200 pence. They have now fallen to 2,700 pence.

I see this as a knife falling through treacle. As patents expire one after the other, earnings will edge downward, and this will put gradual but steady downward pressure on the share price. As there are more patent expirations to come, the share price could yet fall further. So this is another one for the patient. Keep this share on your watchlist and bide your time. Time your move well, and you will be getting a slice of a global pharma giant at a rock-bottom price.

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