Related papers: Continuous-time Duality for Super-replication with…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility…
We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…
As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral…
As load varies continuously over time, it is essential to provide continuous-time price signals that accurately reflect supply-demand balance. However, conventional discrete-time economic dispatch fails to capture the intra-temporal…
Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…
In this paper, we consider the pricing and hedging of a financial derivative for an insider trader, in a model-independent setting. In particular, we suppose that the insider wants to act in a way which is independent of any modelling…
Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous,…
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
We consider the martingale optimal transport duality for c\`adl\`ag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semi-static superhedging strategies) are proved for a class of…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional…
Loyal buyer-seller relationships can arise by design, e.g. when a seller tailors a product to a specific market niche to accomplish the best possible returns, and buyers respond to the dedicated efforts the seller makes to meet their needs.…
We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case…
We study the optimal behavior of a bidder in a real-time auction subject to the requirement that a specified collections of heterogeneous items be acquired within given time constraints. The problem facing this bidder is cast as a…
Derivatives, as a critical class of financial instruments, isolate and trade the price attributes of risk assets such as stocks, commodities, and indices, aiding risk management and enhancing market efficiency. However, traditional hedging…