I would start with "Reverse Mortgage Choices: A Theoretical and Empirical Analysis of the Borrowing Decisions of Elderly Homeowners" Journal of Housing Research , Volume 10, Issue 2. I find the model very interesting and realistic and it includes an useful simulation. http://content.knowledgeplex.org/kp2/kp/kp/text_document_summary/scholarly_article/relfiles/jhr_1002_fratantoni.pdf
One of my colleagues, Martin Seay, has written a paper that might help you in this regard. It is:
Seay, M. C., & Kiss, E. (2014). Understanding reverse mortgages: Do they make sense for you? Fact Sheet (MF3163). Manhattan, KS: K-State Research and Extension.
He is on ResearchGate, and may have this publication included on his page. Anyway, I would reach out to him...he is a very accommodating guy (and smart too).
As an aside, you may also want to check out this short chapter that he and I put together a couple of years ago now:
Seay, M.C., & Carswell, A.T. (2012). Reverse mortgages: A product for an emerging demographic. In A. Tavidze (Ed.), Progress in Economic Research (Vol. 23). Pp. 57-78. Hauppauge, NY: Nova Science Publishers.