Related papers: Topics in Stochastic Portfolio Theory
We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
The topic of this paper is modeling and analyzing dependence in stochastic social networks. Using a latent variable block model allows the analysis of dependence between blocks via the analysis of a latent graphical model. Our approach to…
This paper is a sequel of the reference \cite[\S 4.2, p.p. 1782--1783]{almp}, in where some families of quadratic polynomial vector fields related with orthogonal polynomials were studied. We extend such results that contain some details…
The stock market offers a platform where people buy and sell shares of publicly listed companies. Generally, stock prices are quite volatile; hence predicting them is a daunting task. There is still much research going to develop more…
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
Although the understanding of and motivation behind individual trading behavior is an important puzzle in finance, little is known about the connection between an investor's portfolio structure and her trading behavior in practice. In this…
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation,…
A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
We consider the investor who doesn't trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show…
The $S$ topology on the Skorokhod space was introduced by the author in 1997 and since then it proved to be a useful tool in several areas of the theory of stochastic processes. The paper brings complementary information on the $S$…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
This book consists of a selection of articles divided into three main themes: Statistics, Quantitative Trading, Psychology. These three arguments are indispensable for the development of a quantitative trading system. The order of the…
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with…
Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the properties of their coefficients have been intensively…
Stochastic integrals are defined with respect to a collection $P = (P_i; \, i \in I)$ of continuous semimartingales, imposing no assumptions on the index set $I$ and the subspace of $\mathbb{R}^I$ where $P$ takes values. The integrals are…
We trace the evolution of the theory of stochastic partial differential equations from the foundation to its development, until the recent solution of long-standing problems on well-posedness of the KPZ equation and the stochastic…
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…