En este artículo, los autores pretenden mostrar y explicar cómo la Teoría de Lie se puede aplicar a la resolución de algunos problemas relativos a la Economía y a las Finanzas. Concretamente, se realiza un análisis de dos de esos problemas y se discuten tanto sus aspectos matemáticos como...

In this paper the issue of mathematical programming and optimization has being revisited. The theory of optimization deals with the development of models and methods that determine optimal solutions to mathematical problems defined. Mathematical model must be some function of any solution that...

In this paper I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalizations imply nonconstructive and uncomputable structures. A reasonable and...

A constructive and recursion theoretic analysis of the standard Computable General Equilibrium (CGE) model of economic theory is undertaken. It is shown, contrary to widely expressed views and textbook versions of the CGE model, that the standard CGE model is neither computable nor constructive...

I study connected manifolds and prove that a proper map f: M - M is globally invertible when it has a nonvanishing Jacobian and the fundamental group pi (M) is finite. This includes finite and infinite dimensional manifolds. Reciprocally, if pi (M) is infinite, there exist locally invertible...

We introduce a new approach to model the market smile for inflation-linked derivatives by defining the Quadratic Gaussian Year-on-Year inflation model -- the QGY model. We directly define the model in terms of a year-on-year ratio of the inflation index on a discrete tenor structure, which,...

We propose the eigenfunction expansion method for pricing options in linear-quadratic terms structure models. The eigenvalues, eigenfunctions and adjoint functions are calculated using elements of the representation theory of Lie algebras not only in the self-adjoint case but in non-selfadjoint...

We analyze and compare the performance of the Fourier transform method in affine and quadratic term structure models. We explain why the method of the reduction to FFT in dimension one is efficient for ATSMs of type $A_0(n)$ but may lead to sizable errors for QTSMs unless computational errors...

This paper proposes and studies an optimal placement problem in a limit order book. To gain some analytical insights, a simple correlated random walk model with mean-reversion is proposed for the best ask price. Optimal placement strategies for both single-period and multi-period cases are...