Related papers: On Arbitrage and Duality under Model Uncertainty a…
We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that…
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in…
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 are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…
Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting…
In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an…
We develop a duality theory for the problem of maximising expected lifetime utility from inter-temporal wealth over an infinite horizon, under the minimal no-arbitrage assumption of No Unbounded Profit with Bounded Risk (NUPBR). We use only…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model…
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…
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations,…
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised…
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…
Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from…
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…
No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset…
We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which…
In this paper we extend discrete time semi-static trading strategies by also allowing for dynamic trading in a finite amount of options, and we study the consequences for the model-independent super-replication prices of exotic derivatives.…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump…
In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach to determine option prices and hedging strategies…