Related papers: Model-free bounds for multi-asset options using op…
We establish dual attainment for the multimarginal, multi-asset martingale optimal transport (MOT) problem, a fundamental question in the mathematical theory of model-independent pricing and hedging in quantitative finance. Our main result…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
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…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive…
Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of…
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…
We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
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…
Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of $[0,1]^2$, or the value of a functional of the copula, monotone with…
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…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
We propose a Fundamental Theorem of Asset Pricing and a Super-Replication Theorem in a model-independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as…
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time,…
We obtain distribution-free bounds for various fundamental quantities used in probability theory by solving optimization problems that search for extreme distributions among all distributions with the same mean and dispersion. These…
Existing approaches to asset-pricing under model-uncertainty adapt classical utility-maximization frameworks and seek theoretical comprehensiveness. We move toward practice by considering binary model-risks and by emphasizing 'constraints'…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
We consider a discrete-time incomplete multi-asset market model with continuous price jumps. For a wide class of contingent claims, including European basket call options, we compute the bounds of the interval containing the no-arbitrage…