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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?

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It turns out that you want to maximize profit, which means:

p = X * d - n * m,

p = profit d = discount % n = number of years in the market m = cost to maintain the house per year

Most buyers can't perceive changes in discount of less than 10%, but OTOH, price ranges are inside the buyers heads, so $1 can change the price range in the buyers mind, so you need to talk to potential buyers to understand what price ranges are they considering. This is done by simply asking "what price ranges are you considering?".

Assuming that your house is not overpriced, getting the price down by 10% increments, will considerably reduce your profit, by 10% every time you go down. OTOH, buyers will buy if they consider other buyers can see that your house is a real bargain, and since you are reducing the price, they will see it as great opportunity, just because you are using a simple trick.

So what is the best strategy? Start very high, let us say, 30% over market price, and then reduce the price by 10% every 3 to 6 months. The real reason is that you only have one property so you can't flood the market, you can only skim it, so you need to start high.

How to determine market price? The only real measure is $/sq meters or $/sq feet in your area. All the rest is mumbo jumbo. It doesn't matter if the property is ugly, has an excellent view or if it needs maintenance. That's just how the real state market works, you can add those to the final negotiation, but you never add them when setting the price. Consider that when buying your next house.

What is market price anyway? Whatever people think their houses are valued. And if you post a very high price, you are actually pushing the market up, which makes sense if you are seller, since other sellers will follow you, since all of them investigate the market before setting their price.

Setting the price down 10% every 3 to 6 months will only make buyers hurry up, because once your house gets below market price it will be gone very fast.

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