Related papers: Generalised Lyapunov Functions and Functionally Ge…
We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean,…
Given the surge in popularity of mutual funds (including exchange-traded funds (ETFs)) as a diversified financial investment, a vast variety of mutual funds from various investment management firms and diversification strategies have become…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
We propose a prediction model based on the minority game in which traders continuously evaluate a complete set of trading strategies with different memory lengths using the strategies' past performance. Based on the chosen trading strategy…
A diversified risk-adjusted time-series momentum (TSMOM) portfolio can deliver substantial abnormal returns and offer some degree of tail risk protection during extreme market events. The performance of existing TSMOM strategies, however,…
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…
We propose two novel frameworks to study the price formation of an asset negotiated in an order book. Specifically, we develop a game-theoretic model in many-person games and mean-field games, considering costs stemming from limited…
In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability…
We derive a universal function for the kinetics of complex systems. This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called "fractal kinetic".The concentration evolutionary equation is…
A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price…
In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some…
We review some fundamental concepts of investment from a mathematical perspective, concentrating specifically on fractional-Kelly portfolios, which allocate a fraction of wealth to a growth-optimal portfolio while the remainder collects (or…
Modern portfolio theory has provided for decades the main framework for optimizing portfolios. Because of its sensitivity to small changes in input parameters, especially expected returns, the mean-variance framework proposed by Markowitz…
This work extends a previous work in regime detection, which allowed trading positions to be profitably adjusted when a new regime was detected, to ex ante prediction of regimes, leading to substantial performance improvements over the…
We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of…
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the…
The use of machine learning for statistical modeling (and thus, generative modeling) has grown in popularity with the proliferation of time series models, text-to-image models, and especially large language models. Fundamentally, the goal…
The aim of this survey is twofold. First we show how the Markov tower construction is applicable for obtaining finer stochastic properties, like a local limit theorem of probability theory. Here the fundamental method is the study of the…
This article is a prologue to the article "Why Markets are Inefficient: A Gambling 'Theory' of Financial Markets for Practitioners and Theorists." It presents important background for that article --- why gambling is important, even…
The role of portfolio construction in the implementation of equity market neutral factors is often underestimated. Taking the classical momentum strategy as an example, we show that one can significantly improve the main strategy's features…