Related papers: Topics in Stochastic Portfolio Theory
A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity,…
Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on F{\"o}llmer…
Submitted to F. Schweitzer (ed.), Microscopic Models for Economic Dynamics, Lecture notes in physics, Springer, Berlin-Heidelberg 2002.kiel.tex
In this paper we introduce new models of complex weighted networks sharing several properties with fractal sets: the deterministic non-homogeneous weighted fractal networks and the stochastic weighted fractal networks. Networks of both…
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
A competing market model with a polyvariant profit function that assumes "zeitnot" stock behavior of clients is formulated within the banking portfolio medium and then analyzed from the perspective of devising optimal strategies. An…
This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135 (2011); also available at arXiv:1107.5293v2 [math-ph]].
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…
This paper focuses on stochastic orders and its applications : policy limits and deductibles. Further, many applications and some examples are given : comparison of two families of copulas, individual and collective risk model, reinsurance…
In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then…
In this work, I address the issue of forming riskless hedge in the continuous time option pricing model with stochastic stock volatility. I show that it is essential to verify whether the replicating portfolio is self-financing, in order…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
Domain theory has a long history of applications in theoretical computer science and mathematics. In this article, we explore the relation of domain theory to probability theory and stochastic processes. The goal is to establish a theory in…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
Contents: I. Introduction II. Manifolds in random media III. Thermal fluctuations without disorder IV. Random forces V. Random potential: variational approach VI. Physical interpretation of the solution
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…
Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…