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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…
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…
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…
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…
We introduce a novel neural-network-based approach to learning the generating function $G(\cdot)$ of a functionally generated portfolio (FGP) from synthetic or real market data. In the neural network setting, the generating function is…
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…
This paper presents a synthesis of the theories of portfolio generating functions and option pricing. The theory of portfolio generation is extended to measure the value of portfolios generated by positive C^{2,1} functions of asset prices…
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…
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…
In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a…
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment…
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…
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…
We use pathwise It\^o calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of F\"ollmer's pathwise It\^o calculus and works for…
For a functionally generated portfolio, there is a natural decomposition of the relative log-return into the log-change in the generating function and a drift process. In this note, this decomposition is extended to arbitrary stock…
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…
We propose a novel portfolio trading system, which contains a feature preprocessing module and a trading module. The feature preprocessing module consists of various data processing operations, while in the trading part, we integrate the…
This paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the…
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…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…