41 research outputs found
A random journey through dynamics and finance: pullback attractors, price impact, nonlinear valuation and FX market.
The main objective of this thesis is to explore several areas of Random Dynamical Systems and Mathematical Finance. We start by considering random dynamical systems with two different sources of noise, which we call common and intrinsic. We study the interplay between these two sources of randomness from a novel point of view, going beyond the usual statistical approach. We determine the stochastic Fokker-Planck equation describing the system and prove that such equation has a pullback attractor for almost all realizations of the common noise. On the mathematical finance side, we start by discussing consistency properties of jump-diffusion models with respect to inversion, with applications to the Foreign Exchange market. We first solve the constant jump size case, and then analyze the more involved case of the compound Poisson process. We determine a fairly general class of admissible densities for the jump size in the domestic measure. Then, we delve into the nonlinear valuation framework under credit risk, collateral and funding costs, generalizing the mathematical framework of \cite{brigo2019nonlinear} for what concerns in particular the filtrations and the default times. Finally, we propose a first theory of price impact in presence of an interest-rates term structure. We formulate an instantaneous and transient price impact model for zero-coupon bond, defining a cross price impact that is endogenous to the term structure. We extend this setup to coupon-bearing bonds, HJM framework and conclude by solving an optimal execution problem in interest rates market.Open Acces
Fuzzy Sets, Fuzzy Logic and Their Applications 2020
The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity
Academic Year 2019-2020 Faculty Excellence Showcase, AFIT Graduate School of Engineering & Management
An excerpt from the Dean\u27s Message:
There is no place like the Air Force Institute of Technology (AFIT). There is no academic group like AFIT’s Graduate School of Engineering and Management. Although we run an educational institution similar to many other institutions of higher learning, we are different and unique because of our defense-focused graduate-research-based academic programs. Our programs are designed to be relevant and responsive to national defense needs. Our programs are aligned with the prevailing priorities of the US Air Force and the US Department of Defense. Our faculty team has the requisite critical mass of service-tested faculty members. The unique composition of pure civilian faculty, military faculty, and service-retired civilian faculty makes AFIT truly unique, unlike any other academic institution anywhere
Constructing copulas from shock models with imprecise distributions
The omnipotence of copulas when modeling dependence given marg\-inal
distributions in a multivariate stochastic situation is assured by the Sklar's
theorem. Montes et al.\ (2015) suggest the notion of what they call an
\emph{imprecise copula} that brings some of its power in bivariate case to the
imprecise setting. When there is imprecision about the marginals, one can model
the available information by means of -boxes, that are pairs of ordered
distribution functions. By analogy they introduce pairs of bivariate functions
satisfying certain conditions. In this paper we introduce the imprecise
versions of some classes of copulas emerging from shock models that are
important in applications. The so obtained pairs of functions are not only
imprecise copulas but satisfy an even stronger condition. The fact that this
condition really is stronger is shown in Omladi\v{c} and Stopar (2019) thus
raising the importance of our results. The main technical difficulty in
developing our imprecise copulas lies in introducing an appropriate stochastic
order on these bivariate objects
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more