Related papers: Is the difference between deep hedging and delta h…
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for…
Recent developments in deep learning techniques have motivated intensive research in machine learning-aided stock trading strategies. However, since the financial market has a highly non-stationary nature hindering the application of…
We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural…
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson…
In power markets, Green Power Purchase Agreements have become an important contractual tool of the energy transition from fossil fuels to renewable sources such as wind or solar radiation. Trading Green PPAs exposes agents to price risks…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
Deep hedging trains neural networks to manage derivative risk under market frictions, but produces hedge ratios with no measure of model confidence -- a significant barrier to deployment. We introduce uncertainty quantification to the deep…
We introduce a new methodology that enables detection of the onset of convergence towards Nash equilibria in simple repeated games with infinitely large strategy spaces, thereby revealing the heuristics used in decision-making. The method…
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
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…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning…
We examine two types of binary betting markets, whose primary goal is for profit (such as sports gambling) or to gain information (such as prediction markets). We articulate the interplay between belief and price-setting to analyse both…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
Recently equal risk pricing, a framework for fair derivative pricing, was extended to consider dynamic risk measures. However, all current implementations either employ a static risk measure that violates time consistency, or are based on…
Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the…
In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the…
This paper builds on "Collective Arbitrage and the Value of Cooperation" by Biagini et al. (2025, forthcoming in "Finance and Stochastics"), which introduced in discrete time the notions of collective arbitrage and super-replication in a…