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A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training…
We investigate stability issues for the one-dimensional variant of the celebrated Hughes model for pedestrian evacuation. The cost function is assumed to be affine, which is a setting where existence of solutions with BV loc in space…
Shapley values have become one of the go-to methods to explain complex models to end-users. They provide a model agnostic post-hoc explanation with foundations in game theory: what is the worth of a player (in machine learning, a feature…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
While machine learning methods have significantly improved model performance over traditional methods, their black-box structure makes it difficult for researchers to interpret results. For highly regulated financial industries, model…
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)…
Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…
We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the…
In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying…
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such as coefficient identification in partial differential…
We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this…
A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of…
We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns.…
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
The control function approach allows the researcher to identify various causal effects of interest. While powerful, it requires a strong invertibility assumption in the selection process, which limits its applicability. This paper expands…
In this paper, we study the performance of affine policies for two-stage adjustable robust optimization problem with fixed recourse and uncertain right hand side belonging to a budgeted uncertainty set. This is an important class of…
Multimodal foundation models offer promising advancements for enhancing driving perception systems, but their high computational and financial costs pose challenges. We develop a method that leverages foundation models to refine predictions…