Custom title tag for page included into WordPress

Here’s the skinny. I’m using WordPress to wrap around a custom page of mine, however because it isn’t fully recognized by WordPress, the title HTML tag is blank eg. <title></title>

Is there an easy way, via either a hook or a filter to replace the title tag? I’ve tried the following, but I don’t seem to be on the right track. Any help would be excellent.

function page_title(){

	$output = '<title>Custom Title</title>';
	echo apply_filters('page_title', $output);
}	

add_action('wp_head','page_title');