Related papers: A C\`adl\`ag Rough Path Foundation for Robust Fina…
In this work we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (so-called non-linear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and…
There is often a trade-off between building deep learning systems that are expressive enough to capture the nuances of the reality, and having the right inductive biases for efficient learning. We introduce Residual Pathway Priors (RPPs) as…
We examine the relation between a stochastic version of the rough path integral with the symmetric-Stratonovich integral in the sense of regularization. Under mild regularity conditions in the sense of Malliavin calculus, we establish…
The purpose of these notes is to distribute, mostly without proofs, fundamental definitions and results concerning the theory of semimartingales and stochastic integration. The material serves as a foundational guide for those interested in…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
Inspired by recent advances in singular SPDE theory, we use the Poincar\'e inequality on Wiener space to show that controlled complementary Young regularity is sufficient to obtain Gaussian rough paths lifts. This allows us to completely…
We prove an extension to the classical continuity theorem in rough paths. We show that two $p$-rough paths are close in all levels of iterated integrals provided the first $\lfl p \rfl$ terms are close in a uniform sense. Applications…
For every adapted, c\`agl\`ad process (strategy) $G$ and typical c\`adl\`ag price paths whose jumps satisfy some mild growth condition we define integral $G\cdot S$ as a limit of simple integrals.
With the fast development of quantitative portfolio optimization in financial engineering, lots of AI-based algorithmic trading strategies have demonstrated promising results, among which reinforcement learning begins to manifest…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
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…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
The availability of deep hedging has opened new horizons for solving hedging problems under a large variety of realistic market conditions. At the same time, any model - be it a traditional stochastic model or a market generator - is at…
We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with H\"older exponent greater than 1/2, we…
We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We define the concept of quadratic roughness of a path along a…
We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the…
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…
We study a continuous-time financial market with continuous price processes under model uncertainty, modeled via a family $\mathcal{P}$ of possible physical measures. A robust notion ${\rm NA}_{1}(\mathcal{P})$ of no-arbitrage of the first…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…