22 research outputs found
The fundamental theorem of algebra before Carl Friedrich Gauss
This is a paper about the first attempts of the demonstration of the fundamental theorem of algebra. Before, we analyze the tie between complex numbers and the number of roots of an equation of -n-th degree. In second paragraph we see the relation between the integration and fundamental theorern. Finally, we observe the linear differential equation with constant coefficients and the Euler's position about the fundamental theorem and then we consider the d'Alembert's, Euler's and Laplace's demonstrations. lt is a synthesis paper dedicated to Pere Menal a collegue and a friend
Hedging and pricing European-type claims on non-traded asset using utility maximization
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The Deep Space Network
The functions and facilities of the Deep Space Network, its supporting research and technology and network operations are discussed
Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance
Philosophiae Doctor - PhDOptions are a special type of derivative securities because their values are derived from
the value of some underlying security. Most options can be grouped into either of
the two categories: European options which can be exercised only on the expiration
date, and American options which can be exercised on or before the expiration date.
American options are much harder to deal with than European ones. The reason being
the optimal exercise policy of these options which led to free boundary problems. Ever
since the seminal work of Black and Scholes [J. Pol. Bean. 81(3) (1973), 637-659],
the differential equation approach in pricing options has attracted many researchers.
Recently, numerical singular perturbation techniques have been used extensively for
solving many differential equation models of sciences and engineering. In this thesis,
we explore some of those methods which are based on spline approximations to solve
the option pricing problems. We show a systematic construction and analysis of these
methods to solve some European option problems and then extend the approach to
solve problems of pricing American options as well as some exotic options. Proposed
methods are analyzed for stability and convergence. Thorough numerical results are
presented and compared with those seen in the literature