Related papers: Arbitrage and Hedging in a non probabilistic frame…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
Geometric arbitrage theory reformulates a generic asset model possibly allowing for arbitrage by packaging all asset and their forward dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes…
This thesis develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time finance, does not rely on stochastic integrals or other probabilistic…
The paper investigates quadratic hedging in a semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of…
Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
Employing probabilistic techniques we compute best possible upper and lower bounds on the price of an option on one or two assets with continuous piecewise linear payoff function based on prices of simple call options of possibly distinct…
Real-world data streams can change unpredictably due to distribution shifts, feedback loops and adversarial actors, which challenges the validity of forecasts. We present a forecasting framework ensuring valid uncertainty estimates…
In a Markovian model for a financial market, we characterize the best arbitrage with respect to the market portfolio that can be achieved using nonanticipative investment strategies, in terms of the smallest positive solution to a parabolic…
The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is…
Deep hedging (Buehler et al. 2019) is a versatile framework to compute the optimal hedging strategy of derivatives in incomplete markets. However, this optimal strategy is hard to train due to action dependence, that is, the appropriate…
In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via…
Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero…
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…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…