Related papers: Generalizations of Functionally Generated Portfoli…
Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a…
In this paper, the optimal mean-reverting portfolio (MRP) design problem is considered, which plays an important role for the statistical arbitrage (a.k.a. pairs trading) strategy in financial markets. The target of the optimal MRP design…
Managing investment portfolios is an old and well know problem in multiple fields including financial mathematics and financial engineering as well as econometrics and econophysics. Multiple different concepts and theories were used so far…
We construct a deep portfolio theory. By building on Markowitz's classic risk-return trade-off, we develop a self-contained four-step routine of encode, calibrate, validate and verify to formulate an automated and general portfolio…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that…
In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper…
We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is…
Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…
The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the…
A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general…
The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to…
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to…
Although machine learning approaches have been widely used in the field of finance, to very successful degrees, these approaches remain bespoke to specific investigations and opaque in terms of explainability, comparability, and…
The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…
We provide a simple and straightforward approach to a continuous-time version of Cover's universal portfolio strategies within the model-free context of F\"ollmer's pathwise It\^o calculus. We establish the existence of the universal…