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We argue that contemporary stock market designs are, due to traders' inability to fully express their preferences over the execution times of their orders, prone to latency arbitrage. In turn, we propose a new order type which allows…
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…
In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it…
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…
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy…
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…
Although both data availability and the demand for accurate forecasts are increasing, collaboration between stakeholders is often constrained by data ownership and competitive interests. In contrast to recent proposals within cooperative…
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…
In this paper, we investigate a financial market model consisting of a risky asset, modeled as a general diffusion parameterized by a scale function and a speed measure, and a bank account process with a constant interest rate. This…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
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 apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and…
We develop two alternate approaches to arbitrage-free, market-complete, option pricing. The first approach requires no riskless asset. We develop the general framework for this approach and illustrate it with two specific examples. The…
In this paper, a general framework is developed for continuous-time financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then…
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…
We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated "Arbitrage Pricing Model", we use probabilistic and functional analytic techniques to show the existence of optimal…
We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…