Related papers: Signature Methods in Stochastic Portfolio Theory
In this article we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
We present convincing empirical results on the application of Randomized Signature Methods for non-linear, non-parametric drift estimation for a multi-variate financial market. Even though drift estimation is notoriously ill defined due to…
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized…
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…
We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one. The idea behind Cover's universal portfolio is to build a wealth-weighted average which can be viewed as a buy-and-hold…
Optimal portfolio selection problems are determined by the (unknown) parameters of the data generating process. If an investor wants to realise the position suggested by the optimal portfolios, he/she needs to estimate the unknown…
We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
Signatures, one of the key concepts of rough path theory, have recently gained prominence as a means to find appropriate feature sets in machine learning systems. In this paper, in order to compute signatures directly from discrete data…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete…
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can…
Consider an equity market with $n$ stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio…
A market portfolio is a portfolio in which each asset is held at a weight proportional to its market value. Functionally generated portfolios are portfolios for which the logarithmic return relative to the market portfolio can be decomposed…
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which…
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…
We study market-to-book ratios of stocks in the context of Stochastic Portfolio Theory. Functionally generated portfolios that depend on auxiliary economic variables other than relative capitalizations ("sizes") are developed in two ways,…