Can I have the permanent alimony paid to my ex-spouse continue after death?

Yes, you may do so. You may wish to fund your spouse’s estate for any reason, and you are free to do so. Sometimes, this is done in order to ensure the financial future of the child(ren) above a beyond that of child support. Although, this is maybe not the wisest method, it is sometimes a chosen alternative to additional life insurance policies. If you are considering this, you should consult with a financial advisor.