I asked the same question a couple of years ago. Having used Quicken for years, I wanted something somewhat equivalent. I received a number of suggestions (don't remember app names) and I looked at each of them but couldn't find anything satisfactory. I eventually gave up and bought Parallels, a windows emulator that would allow me to install Quicken on my MBA. This has been a godsend. Quicken works flawlessly running on Parallels, and I've got 2 years of experience with it now to attest to the stability of the pair. Parallels is a great product for just this type of scenario. I initially used Quicken H&B 2012 but have since upgraded to the 2014 version. Both worked well. I hope this helps.
Using virtual machine software to run a specific Windows program (such as Quicken) is a good suggestion. However, Parallels is not a Windows emulator as stated above. It's virtual machine software. There is also VMWare Fusion and VirtualBox which can do the same thing. I recommend using VirtualBox from Oracle because it's free. It doesn't have all the frills that Parallels or Fusion has but it's free and will do the same thing.
You can download VirtualBox for the Mac from here.
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