Are there standard mathematical models for rent vs. buy?

The internet has a lot of "calculators" to decide on rent vs buy. However I think there can be simple mathematical models/formulae to make this decision. I see the following variables, some of which could be modelled as deterministic or stochastic.

1. Inflation Rate
2. Upfront payment, mortgage and annual loan rates
3. Expected return from alternative investments (say equity)
4. House price at time of purchase
5. House price annual appreciation
6. Monthly rent

Are there economic models which provide insights on this problem along these lines?

Based on these variables, do we have threshold conditions which specify when renting is more profitable vis-a-vis buying?