I have several objects in different photos to which I would like to apply the same effects to.
I do not believe it is possible to save a smart filter stack in an easily-accessible manner.
What you can do, is create a template image. Create a new document with layers containing your smart filters. When you need this "stack" of smart filters, open the template image, copy the layer to the document you are working on, and then copy the smart filters to the layer you need.
Yes this is cumbersome. However, I think until Adobe implements some sort of "filter styles" saving, this is about the best you'll get.
As @Scott says in his answer, I don't believe there is a real solution to the problem. I have two different workarounds though:
Create an action
You'll have to recreate each of the smart filters which is annoying, but once you made it, it only takes one click to apply the filters to another smart layer.
Drag the smart filters from one document to another
Open the source document with the stack of smart filters you want to copy and the target document you want to apply them to. Tile the windows so both documents are visible. Convert the background layer in the target document to a smart layer. Drag and drop the stack of smart filters from the source document to the target document.