Related papers: Topics in Stochastic Portfolio Theory
This paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio…
We introduce polynomial processes in the sense of [8] in the context of stochastic portfolio theory to model simultaneously companies' market capitalizations and the corresponding market weights. These models substantially extend volatility…
The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return…
I discuss some theoretical results with a view to motivate some practical choices in portfolio optimization. Even though the setting is not completely general (for example, the covariance matrix is assumed to be non-singular), I attempt to…
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that…
With the good development in the financial industry, the market starts to catch people's eyes, not only by the diversified investing choices ranging from bonds and stocks to futures and options but also by the general "high-risk,…
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of…
This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies…
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using…
Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining,…
We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas…
Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently…
Investment approaches in financial instruments have been varied and often produce unpredictable results. Many investors in the earlier days of investment banking suffered catastrophical losses due to poor strategy and lack of understanding…
In the framework of stochastic portfolio theory we introduce rank volatility stabilized models for large equity markets over long time horizons. These models are rank-based extensions of the volatility stabilized models introduced by…
First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed…
Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact…
In this paper, we provide a comprehensive review of recent advances in robust portfolio selection problems and their extensions, from both operational research and financial perspectives. A multi-dimensional classification of the models and…
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market…
In finance industry portfolio construction deals with how to divide the investors' wealth across an asset-classes' menu in order to maximize the investors' gain. Main approaches in use at the present are based on variations of the classical…