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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…
Let $\psi$ be a multi-dimensional random variable. We show that the set of probability measures $\mathbb{Q}$ such that the $\mathbb{Q}$-martingale $S^{\mathbb{Q}}_t=\mathbb{E}^{\mathbb{Q}}\left[\psi\lvert\mathcal{F}_{t}\right]$ has the…
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…
Supermartingales are here defined on a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators one of them providing a…
We apply Geometric Arbitrage Theory to obtain results in mathematical finance for credit markets, which do not need stochastic differential geometry in their formulation. We obtain closed form equations involving default intensities and…
In 1999 Robert Fernholz observed an inconsistency between the normative assumption of existence of an equivalent martingale measure (EMM) and the empirical reality of diversity in equity markets. We explore a method of imposing diversity on…
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…
Contrary to the widely believed hypothesis that larger, denser cities promote socioeconomic mixing, a recent study (Nilforoshan et al. 2023) reports the opposite behavior, i.e. more segregation. Here, we present a game-theoretic model that…
We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random…
Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset,…
We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study…
We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset…
We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find…
We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of [Kabanov, Y., Hedging and…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson (1965) we formulate this…
We show that in a financial market given by semimartingales an arbitrage opportunity, provided it exists, can only be exploited through short selling. This finding provides a theoretical basis for differences in regulation for financial…
The goal of this paper is to prove a result conjectured in F\"ollmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular…