Related papers: A Relation between Short-Term and Long-Term Arbitr…
Long-term relative arbitrage exists in markets where the excess growth rate of the market portfolio is bounded away from zero. Here it is shown that under a time-homogeneity hypothesis this condition will also imply the existence of…
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…
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…
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 derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation,…
We consider a continuous-time game-theoretic model of an investment market with short-lived assets and endogenous asset prices. The first goal of the paper is to formulate a stochastic equation which determines wealth processes of investors…
This article introduces the notion of arbitrage for a situation involving a collection of investments and a payoff matrix describing the return to an investor of each investment under each of a set of possible scenarios. We explain the…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
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…
This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage…
Statistical arbitrage methods identify mispricings in securities with the goal of building portfolios which are weakly correlated with the market. In pairs trading, an arbitrage opportunity is identified by observing relative price…
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…
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,…
The capitalization-weighted total relative variation $\sum_{i=1}^d \int_0^\cdot \mu_i (t) \mathrm{d} \langle \log \mu_i \rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $\mu_i (\cdot)$…
We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
In practice there are temporary arbitrage opportunities arising from the fact that prices for a given asset at different stock exchanges are not instantaneously the same. We will show that even in such an environment there exists a…