Projective market model approach to AHP decision making

In this paper, we describe market in the projective geometry language and give the definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to the projective geometry formalism and generalise it to an intransitive case. We give financial interpretations of such a generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications for such an extended model.

[1]  Edward W. Piotrowski,et al.  Geometry of financial markets—Towards information theory model of markets , 2006 .

[2]  M. Kwiesielewicz.  The logarithmic least squares and the generalized pseudoinverse in estimating ratios , 1996 .

[3]  Christian Genest,et al.  Hilbert's metric and the analytic hierarchy process , 1996 .

[4]  Luis G. Vargas.  An overview of the analytic hierarchy process and its applications , 1990 .

[5]  R. Kalaba,et al.  A comparison of two methods for determining the weights of belonging to fuzzy sets , 1979 .

[6]  Robert H. Lewis,et al.  Solving the Least Squares Method problem in the AHP for 3 × 3 and 4 × 4 matrices ⋆ , 2005 .

[7]  G. Crawford,et al.  A note on the analysis of subjective judgment matrices , 1985 .

[8]  The matrix rate of return , 2006, physics/0607175.

[9]  Edward W. Piotrowski,et al.  Quantum cat's dilemma: an example of intransitivity in a quantum game , 2006 .

[10]  Saul I. Gass,et al.  The Analytic Hierarchy Process - An Exposition , 2001, Oper. Res..

[11]  Edward W. Piotrowski,et al.  CAT'S DILEMMA — TRANSITIVITY VS. INTRANSITIVITY , 2004 .

[12]  M. Bohanec,et al.  The Analytic Hierarchy Process , 2004 .

[13]  J. Sladkowski.  Giffen paradoxes in quantum market games , 2002 .

[14]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[15]  Thomas L. Saaty,et al.  Marketing Applications of the Analytic Hierarchy Process , 1980 .

[16]  T. Saaty.  Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP) , 2004 .