Related papers: Pathwise stochastic integrals for model free finan…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
Nested stochastic modeling has been on the rise in many fields of the financial industry. Such modeling arises whenever certain components of a stochastic model are stochastically determined by other models. There are at least two main…
In this paper we consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include, among others, the Hansen-Jagannathan (HJ)…
Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically…
We establish a new scale of $p$-variation estimates for martingale paraproducts, martingale transforms, and It\^o integrals, of relevance in rough paths theory, stochastic, and harmonic analysis. As an application, we introduce rough…
We argue that spanning large numbers of degrees of freedom in empirical analysis allows better characterizations of effects and thus improves the trustworthiness of conclusions. Our ideas are illustrated in three studies: equity premium…
We present a new, recursive approach to stochastic inflation which is self-consistent and solves multiple problems which plagued a certain number of previous studies, in particular in realistic contexts where the background spacetime is…
Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
"Model-free" control and the related "intelligent" proportional-integral (PI) controllers are successfully applied to freeway ramp metering control. Implementing moreover the corresponding control strategy is straightforward. Numerical…
Trajectory planning in dense, interactive traffic scenarios presents significant challenges for autonomous vehicles, primarily due to the uncertainty of human driver behavior and the non-convex nature of collision avoidance constraints.…
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 long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal…
Recent progress in the development of efficient computational algorithms to price financial derivatives is summarized. A first algorithm is based on a path integral approach to option pricing, while a second algorithm makes use of a neural…
We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
From the path integral formalism for price fluctuations with non-Gaussian distributions I derive the appropriate stochastic calculus replacing Ito's calculus for stochastic fluctuations.