Yes you can create a list in host web. The only thing is you need to give "Manage" right to web in your AppManifest.xml.
Using REST the code will be:
jQuery.ajax({
url: “http://site url/_api/web/lists”,
type: "POST",
data: JSON.stringify({ '__metadata': { 'type': 'SP.List' }, 'AllowContentTypes': true, 'BaseTemplate': 100, 'ContentTypesEnabled': true, 'Description': 'My list description', 'Title': 'Test' }),
headers: {
"accept": "application/json;odata=verbose",
"content-type": "application/json;odata=verbose",
"content-length": length of post body,
"X-RequestDigest": $("#__REQUESTDIGEST").val()
},
success: doSuccess,
error: doError
});
Check this msdn link for complete details.