Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Push button parliament–why India needs a non-partisan, recorded vote system

Decisions of national importance are made by Parliamentary voting. Yet Indian Members of Parliament (MPs) vote with a remarkable lack of freedom and accountability. The introduction of the Tenth Schedule in the Constitution has crippled free expression, since it provides that MPs voting against ‘any direction’ of their Party are liable to disqualification from the legislature  In addition, except for Constitutional amendments, Indian Parliamentary Procedure Rules do not require votes of MPs to be recorded unless the Speaker’s decision is contested in the House. The result is that voting in the House has become mechanical, controlled by Party politics and devoid of responsibility. This paper comments on a general theory of democratic accountability through the lens of Parliamentary voting. It suggests that the voting system adopted in the Parliament is an effective indicator to measure the level of accountability of its Members. In the context of India, this paper argues that the level of accountability will increase to a desirable extent only when there is adoption of a recorded system for every important House vote. Upon examination of India’s record thus far (through the sample of the 14th Lok Sabha) it becomes evident that the level of divisions (recorded votes) is substantially lower than other countries. This leads the paper to probe, as to why that might be the case. Part II of the paper answers that question by examining the Tenth Schedule of the Constitution. The paper scrutinizes the disproportionate influence of the Party in decision making in the Parliament. Apart from dealing with the inherent problem of the Tenth Schedule, this paper suggests two procedural changes to make parliamentary expression more meaningful. Firstly, the recording of all important votes within the Parliament and secondly, registering Party whips with the Minister of Parliamentary Affairs so that the voter knows the clear stand of every Parliamentary continuum. The focus of the paper is thus to bring back the attention of the legislators to their central function, which is deliberation on and the passage of legislation.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Energy saving innovations, non-exhaustible sources of energy and long-run: what would happen if we run out of oil?

We formulate and solve a model of factor saving technological improvement considering three factors of production: labor, capital and energy. The productive activities have three main characteristics: first, in order to use capital goods firms need energy; second, there are two sources of energy: non-exhaustible and exhaustible; third, capital goods can be of different qualities and the quality of these goods can be changed along two dimensions -reducing the need of energy or changing the source of energy used in the production process. The economy goes through three stages of development after industrialization. In the first, firms make use of exhaustible energy and the e¢ ciency in the use of energy is constant. In the second stage, as the price of energy grows the e¢ ciency in its use is increased. In the third stage, the price of exhaustible sources is so high that firms have incentives to use non-exhaustible sources of energy. During this stage the price of energy is constant. In this set up, the end of the oil age has level effects on consumption and output but it does not cause the collapse of the economic system.