While there’s no Double.max, it is defined in the C float.h header, which you can access in Swift via import Darwin.
import Darwin
let fmax = FLT_MAX
let dmax = DBL_MAX
These are roughly 3.4 * 10^38 and 1.79 * 10^308 respectively.
But bear in mind it’s not so simple with floating point numbers (it’s never simple with floating point numbers). When holding numbers this large, you lose precision in a similar way to losing precision with very small numbers, so:
let d = DBL_MAX
let e = d - 1.0
let diff = d - e
diff == 0.0 // true
let maxPlusOne = DBL_MAX + 1
maxPlusOne == d // true
let inf = DBL_MAX * 2
// perhaps infinity is the “maximum”
inf == Double.infinity // true
So before you get into some calculations that might possibly brush up against these limits, you should probably read up on floating point. Here and here are probably a good start.