A computer-assisted expert algorithm for real estate valuation in Spanish cities

Some of the most overlooked valuation systems in current literature are those based on expert algorithms. Yet these algorithms can form the basis of a good estimation of the value of real estate since they allow simple computational methods that use big data to be integrated with the appraiser’ own knowledge of the situation. The main usefulness of the methodology is an ongoing mortgage risk appraisal for banking institutions. The current expert algorithms based on the sales comparison approach use the arithmetic mean of the comparable prices. But this mean gives equal importance to all neighbouring dwellings instead of giving more importance to those dwellings which are more similar and are nearer to the target dwelling. Improving the classical arithmetic mean or the more robust median, this article proposes a computer-assisted expert algorithm which includes a weighted estimator able to consider the differences in characteristics compared to similar properties and their relative locations. It allows to estimate, in a simple and rapid way using objective criteria, the value of any residential property in Spain. The results show good fit for large cities in terms of the usual error margins while improving the results with regards to smaller cities. In all cases, in terms of mean absolute percentage error, the weighted estimator improves the arithmetic mean or median results.

Universal modification of vector weighted method of correlated sampling with finite computational cost

The weighted method of dependent trials or weighted method of correlated sampling (MCS) allows one to construct estimators for functionals based on the same Markov chain simultaneously for a given range of the problem parameters. Choosing an appropriate Markov chain, it is necessary to take into account additional conditions providing the finiteness of the computational cost of weighted MCS. In this paper we study the issue of finite computational cost of the method of correlated sampling (MCS) in application to evaluation of linear functionals of solutions to a set of systems of 2nd kind integral equations. A universal modification of the vector weighted MCS is constructed providing the branching of chain trajectory according to elements of matrix weights. It is proved that the computational cost of the constructed algorithm is bounded in the case the base functionals are also bounded. The results of numerical experiments using the modified weighted estimator are presented for some problems of the theory of radiation transfer subject to polarization.