Dynamic delta hedging of autocallables under a discrete rebalancing context

This work tests different delta hedging strategies for two products issued by Banco de Investimento Global in 2012. The work studies the behaviour of the delta and gamma of autocallables and their impact on the results when delta hedging with different rebalancing periods. Given its discontinuous payoff and path dependency, it is suggested the hedging portfolio is rebalanced on a daily basis to better follow market changes. Moreover, a mixed strategy is analysed where time to maturity is used as a criterion to change the rebalancing frequency.

On the pricing of bivariate options in the presence of a discrete dividend payment

A Work Project, presented as part of the requirements for the Award of a Master's Double Degree in Finance from the NOVA School of Business and Economics / Masters Degree in Economics from Insper

The accuracy of the escrowed dividend model on the value of European options on a stock paying discrete dividend

This project characterizes the accuracy of the escrowed dividend model on the value of European options on a stock paying discrete dividend. A description of the escrowed dividend model is provided, and a comparison between this model and the benchmark model is realized. It is concluded that options on stocks with either low volatility, low dividend yield, low ex-dividend to maturity ratio or that are deep in or out of the money are reasonably priced with the escrowed dividend model.

Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Numerical investigation of micro and macro mechanical behaviour of granular media via a discrete element approach

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009

Global eriodicity and complete integrability of discrete dynamical systems

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Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Limit Cycles for a class of three dimensional polynomial differential systems

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Polynomial and linearized normal forms for almost periodic differential systems

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On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Ataxia telangiectasia mutated (ATM) inhibition transforms human mammary gland epithelial cells.

Carriers of mutations in the cell cycle checkpoint protein kinase ataxia telangiectasia mutated (ATM), which represent 1-2% of the general population, have an increased risk of breast cancer. However, experimental evidence that ATM deficiency contributes to human breast carcinogenesis is lacking. We report here that in MCF-10A and MCF-12A cells, which are well established normal human mammary gland epithelial cell models, partial or almost complete stable ATM silencing or pharmacological inhibition resulted in cellular transformation, genomic instability, and formation of dysplastic lesions in NOD/SCID mice. These effects did not require the activity of exogenous DNA-damaging agents and were preceded by an unsuspected and striking increase in cell proliferation also observed in primary human mammary gland epithelial cells. Increased proliferation correlated with a dramatic, transient, and proteasome-dependent reduction of p21(WAF1/CIP1) and p27(KIP1) protein levels, whereas little or no effect was observed on p21(WAF1/CIP1) or p27(KIP1) mRNAs. p21(WAF1/CIP1) silencing also increased MCF-10A cell proliferation, thus identifying p21(WAF1/CIP1) down-regulation as a mediator of the proliferative effect of ATM inhibition. Our findings provide the first experimental evidence that ATM is a human breast tumor suppressor. In addition, they mirror the sensitivity of ATM tumor suppressor function and unveil a new mechanism by which ATM might prevent human breast tumorigenesis, namely a direct inhibitory effect on the basal proliferation of normal mammary epithelial cells.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

The convenient calculation of some test statistics in models of discrete choice

The paper considers the use of artificial regression in calculating different types of score test when the log