On Wednesday, June 20 the all-Russian seminar "Mathematical methods of decision analysis in economics, finance and politics" was hold.

Speaker: V.R. Evstigneev (HSE)
Title: "Probabilistic picture of the world: how the intuitive perception of price process in the foreign exchange market is born and evolves"

Speaker: V.R. Evstigneev (HSE)

Title: "Probabilistic picture of the world: how the intuitive perception of price process in the foreign exchange market is born and evolves"

 

Abstract: The motivation of the research is to build a time evolution operator of subjective expectations of players in the foreign exchange markets preserving the norm and providing a systematic circulation of average yield. For this purpose we consider the Fokker - Planck equation, parametrized by function of the instantaneous diffusion and instantaneous shift and solved by the separation of variables. In the course of this scenario a new way of solving the Sturm - Liouville equation is proposed to endogenously obtain a function of instanteous displacement for a given function of instantaneous diffusion. On this basis we obtain a system of polynomial solutions of the corresponding second order differential equation and its adjoint equation. Using the equivalence of the Sturm - Liouville and Euler - Lagrange equations, we solve the inverse variational problem of finding the weight function corresponding to this polynomial solution of the Sturm - Liouville problem. Considering each weight function as a probability density, we obtain a system of orthonormal polynomials with Hankel and Hamburger matrix of moments of this function (problem of Stieltjes - Hamburger), these polynomials are basic functions and define a linear space for the continuous case, allowing the operator to build the integral transformation of Fredholm type empirical function probability density for the discrete case and allow to obtain a unitary operator. Unitary transformation of empirical vectors of yield values allows us to build a highly efficient forecasts of price process in the forex market.