Related papers: Robust Fundamental Theorem for Continuous Processe…
We formulate a superhedging theorem in the presence of transaction costs and model uncertainty. Asset prices are assumed continuous and uncertainty is modelled in a parametric setting. Our proof relies on a new topological framework in…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no…
We consider an incomplete multi-asset binomial market model. We prove that for a wide class of contingent claims the extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure. This allows…
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to…
The problem of robust dynamic pricing of an abstract commodity, whose inventory is specified at an initial time but never subsequently replenished, originally studied by Perakis and Sood (2006) in discrete time, is considered from the…
We establish deterministic necessary and sufficient conditions for the no-arbitrage notions "no increasing profit" (NIP), "no strong arbitrage" (NSA) and "no unbounded profit with bounded risk" (NUPBR) in one-dimensional general diffusion…
We develop a theory which applies to any market dynamics that satisfy a fair market assumption on the nullity of the average profit of simple market making strategies. We show that for any such fair market, there exists a martingale fair…
We introduce, in continuous time, an axiomatic approach to assign to any financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity)…
We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…
We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual…
We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\langle X \rangle$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest…
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 study the situation of an agent who can trade on a financial market and can also transform some assets into others by means of a production system, in order to price and hedge derivatives on produced goods. This framework is motivated by…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…
We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure.…