I have a real world problem and I was wondering if you guys have any nice insight on the best way to solve it mathematically. I'm not sure there is a decisive solution, but it would be nice to have a decent approximation.
So there is a house being sold for X dollars and has been on the market for a while. The price could be lowered to Y dollars which would likely lead to an earlier sale, but would be a lower profit.
Assuming that there is a maintenance cost of m dollars a year while the house remains unsold and that the interest gained on the sale money would be i. How would one go about estimating how long it would be reasonable to wait before lowering the price of the house from X to Y?
I think the simplest model would be to assign some estimate on the probability of selling the house but I'm not 100% clear on how to calculate the expected value given that the price switched from X to Y at time t.
The other possibility that came to mind was somehow using a markov chain. On that I am completely lost. I haven't the slightest idea about how to start that.
Any ideas on how to move forward, or better ideas than the ones I've had?