A NOTE ON COMONOTONICITY AND POSITIVITY OF THE CONTROL COMPONENTS OF DECOUPLED QUADRATIC FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth

The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results on the numerical methods for FBSDEs relies on the global Lipschitz assumption, which is not satisfied for a number of important cases such as the Fisher--KPP or the FitzHugh--Nagumo equations. Furthermore, it has been shown in \cite{LionnetReisSzpruch2015} that for BSDEs with monotone drivers having polynomial growth in the primary variable $y$, only the (sufficiently) implicit schemes converge. But these require an additional computational effort compared to explicit schemes. This article develops a general framework that allows the analysis, in a systematic fashion, of the integrability properties, convergence and qualitative properties (e.g.~comparison theorem) for whole families of modified explicit schemes. The framework yields the convergence of some modified explicit scheme with the same rate as implicit schemes and with the computational cost of the standard explicit scheme. To illustrate our theory, we present several classes of easily implementable modified explicit schemes that can computationally outperform the implicit one and preserve the qualitative properties of the solution to the BSDE. These classes fit into our developed framework and are tested in computational experiments.Comment: 49 pages, 3 figure

On Securitization, Market Completion and Equilibrium Risk Transfer

We propose an equilibrium framework within which to price financial securities written on non- tradable underlyings such as temperature indices. We analyze a financial market with a finite set of agents whose preferences are described by a convex dynamic risk measure generated by the solution of a backward stochastic differential equation. The agents are exposed to financial and non-financial risk factors. They can hedge their financial risk in the stock market and trade a structured derivative whose payoff depends on both financial and external risk factors. We prove an existence and uniqueness of equilibrium result for derivative prices and characterize the equilibrium market price of risk in terms of a solution to a non-linear BSDE.Backward stochastic differential equations, dynamic risk measures, partial equilibrium, equilibrium pricing, market completion

Challenges and opportunities of implementing a ,mobile bank in Portugal by Altice Group

This research intends to provide a deeper overview of the market challenges and opportunities of establishing a mobile bank in Portugal by Altice Group, through the investigation of the main forces that are disrupting the industry, combining with a market research through an online questionnaire that adds evidence in those findings and provides deeper view of the Portuguese market. With this research the company is able to understand how it can add value to the industry and which future business model is proposed

Large Deviations and Exit-times for reflected McKean-Vlasov equations with self-stabilizing terms and superlinear drifts

We study a class of reflected McKean-Vlasov diffusions over a convex domain with self-stabilizing coefficients. This includes coefficients that do not satisfy the classical Wasserstein Lipschitz condition. Further, the process is constrained to a (not necessarily bounded) convex domain by a local time on the boundary. These equations include the subclass of reflected self-stabilizing diffusions that drift towards their mean via a convolution of the solution law with a stabilizing potential. Firstly, we establish existence and uniqueness results for this class and address the propagation of chaos. We work with a broad class of coefficients, including drift terms that are locally Lipschitz in spatial and measure variables. However, we do not rely on the boundedness of the domain or the coefficients to account for these non-linearities and instead use the self-stabilizing properties. We prove a Freidlin-Wentzell type Large Deviations Principle and an Eyring-Kramer's law for the exit-time from subdomains contained in the interior of the reflecting domain.Comment: 41 page

Equilibrium pricing under relative performance concerns

We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). Each agent is not only exposed to financial and non-financial risk factors, but she also faces performance concerns with respect to the other agents. Within our proposed model we prove the existence and uniqueness of an equilibrium whose analysis involves systems of fully coupled multi-dimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a non-standard aggregation of risk measures is possible via weighted-dilated infimal convolution. We analyze the impact of the problem's parameters on the pricing mechanism, in particular how the agents' performance concern rates affect prices and risk perceptions. In extreme situations, we find that the concern rates destroy the equilibrium while the risk measures themselves remain stable

Construção do edifício Báltico Center, Parque das Nações

É uma inevitabilidade que, mesmo num curso de engenharia, a vertente académica seja preponderante sobre a vertente académica. A evolução dos materiais, das tecnologias e da própria construção a isso obrigam. No entanto, para se poder perceber os impactes dessa evolução, torna-se necessário ver in loco a sua aplicação. Assim, após seis anos de curso, um estágio numa empresa de construção foi o passo que me pareceu mais lógico e enriquecedor. O facto de ser em obra propôs-me um desafio extra por ser uma actividade com uma dinâmica totalmente diferente da que estava habituado. As 16 semanas de estágio foram essenciais para adquirir experiência e alguns conhecimentos extremamente úteis na futura vida profissional. Pretende-se, com este relatório, resumir de uma forma simples mas completa, essa experiência, descrevendo, ao longo de quatro capítulos, o projecto, as soluções técnicas propostas para resolver alguns problemas encontrados, a vivência de trabalhar numa obra e a sua organização; e, por último, uma solução de planeamento e gestão da obra inovadora em Portugal: o Building Information Modelling (B.I.M.)

FBSDE with time delayed generators: Lp-solutions, differentiability, representation formulas and path regularity

We extend some works of Delong and Imkeller concerning Backward stochastic differential equations with time delayed generators (delay BSDE). We provide sharper a priori estimates and show that the solution of a delay BSDE is in $L^p$. We introduce decoupled systems of SDE and delay BSDE (which we term delay FBSDE) and give sufficient conditions for the variational differentiability of their solutions. We connect these derivatives to the Malliavin derivatives of such delay FBSDE via the usual representation formulas which in turn give access to several path regularity results. In particular we prove an extension of the $L^2$-path regularity result for delay FBSDE