No, there is no event like "cursor position changed".

But if you want to know if the cursor position changed, you can do something like this:
tested with jquery 1.7, i tested in Ie8 and chrome

var last_position = 0;

$(document).ready(function () {

    $("#my_input").bind("keydown click focus", function() {

        console.log(cursor_changed(this));

    });

});

the console.log will return when the cursor have changed.

function cursor_changed(element) {

    var new_position = getCursorPosition(element);

    if (new_position !== last_position) {

        last_position = new_position;

        return true;

    }

        return false;

}



function getCursorPosition(element) {

    var el = $(element).get(0);

    var pos = 0;

    if ('selectionStart' in el) {

        pos = el.selectionStart;

    } else if ('selection' in document) {

        el.focus();

        var Sel = document.selection.createRange();

        var SelLength = document.selection.createRange().text.length;

        Sel.moveStart('character', -el.value.length);

        pos = Sel.text.length - SelLength;

    }

    return pos;

}