To list the logged in author’s posts and put an edit link after each title, you can use the following function:

function logged_in_author_posts(){
	if( ! is_user_logged_in() )
		return false;

	$query = new WP_Query( array(
		'post_type'      => 'post',
		'author'         => get_current_user_id(),
		'post_status'    => 'publish',
		'posts_per_page' => -1
	));

	if( $query->have_posts() ):
		echo '<h2>Your posts</h2>';
		echo '<ul>';
		while ( $query->have_posts() ) : $query->the_post();
			echo '<li>';
			the_title();
			edit_post_link( __('Edit'), ' <span>', '</span>' );
			// the_excerpt();
			echo '</li>';
		endwhile;
		echo '</ul>';
		wp_reset_postdata();
	endif;
}

You can take out the double-slash ‘//’ from // the_excerpt(); to show the post excerpt.
Note: we use a new WP_Query instance here instead of the old query_posts() function, as query_posts() modifies the main query and is discouraged. wp_reset_postdata() restores the global post data after our custom loop.

Now you can use logged_in_author_posts() anywhere in your theme to display the list. The list will only appear if the user is logged in and has at least one published post.

logged_in_author_posts();