Pricing in the Real Estate Market as a Stochastic Limit. Log Normal Approximation

We construct a stochastic model of real estate pricing. The method of the pricing construction is based on a sequential comparison of supply prices. We prove that under standard assumptions imposed upon the comparison coefficients there exists a unique non-degenerate limit in distribution and this limit has a Log Normal law of distribution. We verify agreement between empirical distributions of prices and theoretically obtained Log Normal distribution by numerous statistical data of real estate prices from Saint-Petersburg (Russia). To establish this accordance we essentially apply the efficient and sensitive test of fit of Kolmogorov-Smirnov. Basing on the world admitted standard of estimation prices in real estate market, we conclude that the most probable price, i.e. mode of distribution, is correctly and uniquely determined under the Log Normal approximation. Since the mean value of a Log Normal distribution exceeds the mode -- most probable value, it follows that the prices valued by the mathematical expectation are systematically overstated.