Related papers: From small markets to big markets
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic…
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of…
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it…
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…
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…
We study the optimal control of storage which is used for arbitrage, i.e. for buying a commodity when it is cheap and selling it when it is expensive. Our particular concern is with the management of energy systems, although the results are…
Polymarket is a prediction market platform where users can speculate on future events by trading shares tied to specific outcomes, known as conditions. Each market is associated with a set of one or more such conditions. To ensure proper…
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations…
We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently…
Buying and selling of data online has increased substantially over the last few years. Several frameworks have already been proposed that study query pricing in theory and practice. The key guiding principle in these works is the notion of…
This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…
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…
Posted price mechanisms are prevalent in allocating goods within online marketplaces due to their simplicity and practical efficiency. We explore a fundamental scenario where buyers' valuations are independent and identically distributed,…
We study the problem of maximising terminal utility for an agent facing model uncertainty, in a frictionless discrete-time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the…