why stack pointer is initialized to the maximum value?
I only knows that It is the tiny register which stores the last program request’s address in a stack. It is the particular kind of buffer that stores the information in the order of top-down. but can anyone explain me why initially it's having max value.
Without more detail on the actual microprocessor, there isn't a single exact answer; but in general, each architecture handles stack pointer initialization a bit differently. For example, the version of ARM used in many microprocessors initializes the stack pointer (also R13) from the vector table (the first entry). Other architectures either initialize the register to 0 or some other value; so it's not always all 1s as you mention in your question. If the hardware itself doesn't initialize the stack pointer so somewhere meaningful, some of the first instructions usually does. And usually this value is near or at the top of memory as you mention, the stack typically grows down from higher addresses to lower ones; so a value of all 1s or some other larger value might make sense depending on how memory is laid out and managed.
One thing also worth mentioning is that you say the stack stores the "last program request's address" which if I understand correctly is one of the things the stack stores. In more architectures, the stack can store much more than just the return address of a call but also local variables, saved context when a call is made or a context is swapped (either by an OS or by an exception/interrupt) and anything else the program might want to push onto it.
So the short answer is: it isn't always set to the maximum value but it's usually set to some high value as the stack will grow down to lower addresses as things like data and addresses are pushed on it.