There are still plenty of ASX shares I would be happy to buy despite the recent market volatility.
Some are trading at more attractive prices after pullbacks. Others continue to look like high-quality long-term options, even if they are not obvious bargains.
If I had $5,000 to put to work this week, three ASX shares I would be looking at closely are named in this article.

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Hub24 Ltd (ASX: HUB)
The first ASX share I would buy is Hub24.
Hub24 is one of the standout platform businesses on the ASX. It provides technology that helps financial advisers manage client portfolios, administration, reporting, and investment access.
What I like about Hub24 is that it sits behind the scenes in a large and growing wealth industry.
Australians are building wealth through superannuation, property, shares, inheritance, and retirement savings. Many people need advice as their financial lives become more complicated. Advisers, in turn, need better systems to serve clients efficiently.
That is where Hub24 has been winning.
The company has built a strong reputation for service, functionality, and innovation. Once advisers use a platform and build client processes around it, those relationships can become hard to shift.
Hub24 will still be affected by market movements, as weaker share markets can reduce funds under administration. But over the long term, I think the shift toward modern investment platforms remains very attractive.
Codan Ltd (ASX: CDA)
The second ASX share I would consider is Codan.
Codan is an interesting mix of businesses. It is known for metal detection through Minelab, but it also has a growing communications and technology side through Zetron and Domo Tactical Communications.
That combination gives investors exposure to more than one theme.
Minelab can benefit when gold prices are strong and demand for gold detectors improves. But the communications side is increasingly important, particularly in areas such as public safety, defence, security, and mission-critical communications.
I like Codan because it has a history of finding specialist markets and building strong positions inside them.
It is not trying to be everything to everyone. It makes products for customers that need reliability in difficult environments. That can create pricing power and brand strength if the technology performs well.
The share price can be cyclical, especially because gold detector demand can move around. But I think Codan's broader technology base gives it a stronger long-term story than the market sometimes appreciates.
Commonwealth Bank of Australia (ASX: CBA)
The third ASX share I would buy is Commonwealth Bank of Australia.
CBA remains the highest-quality major bank in Australia in my view. It has enormous scale, a powerful deposit base, strong digital capability, and deep customer relationships.
The recent share price weakness has made the buying case more appealing.
CBA is still not a bargain-basement stock, and investors are usually asked to pay a premium for its quality. But I think that premium is understandable.
The bank has a long record of generating strong profits, paying large fully franked dividends, and maintaining a strong position in home lending, deposits, and business banking.
The economic backdrop is more challenging now, with households dealing with cost-of-living pressure and interest rates. That could keep bank shares volatile.
But if I were investing for the next five to 10 years, CBA is the kind of blue-chip share I would be comfortable holding through the cycle.
Foolish takeaway
For me, the appeal of these three ASX shares is that each has a clear reason to exist in a long-term portfolio. They are not chasing the same opportunity, and they are not all exposed to the same risks.
In a market that can swing quickly from optimism to caution, I think shares like these are worth considering.