Sarah Kaakaï | Searcharxiv

arXiv2026

Nonparametric hazard rate estimation with associated kernels and minimax bandwidth choice

In this paper, we introduce a general theoretical framework for nonparametric hazard rate estimation using associated kernels, whose shapes depend on the point of estimation. Within this framework, we establish rigorous asymptotic results, including a second-order expansion of the MISE, and a central limit theorem for the proposed estimator. We also prove a new oracle-type inequality for both local and global adaptive bandwidth selection, extending the Goldenshluger-Lepski method to the context of associated kernels. Our results propose a systematic way to construct and analyze new associated kernels. Finally, we show that the general framework applies to the Gamma kernel, and we provide several examples of applications on simulated data and experimental data for the study of aging.

math.ST↗

arXiv2024

Deep learning scheme for forward utilities using ergodic BSDEs

In this paper, we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model. For this purpose, we use the representation of dynamic consistent utilities with mean of ergodic Backward Stochastic Differential Equations (eBSDEs) introduced by Liang and Zariphopoulou in [27]. We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time $τ$ , defined as the hitting time of the positive recurrent stochastic factor V . The viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost $λ$ which is a part of the solution of the eBSDEs. In particular, for a certain class of eBSDEs with quadratic generator, the Cole-Hopf transform leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost $λ$. The latter can be estimated with Monte Carlo methods. We also propose two new deep learning numerical schemes for eBSDEs, where the ergodic cost $λ$ is optimized according to a loss function at the random horizon $τ$ or taking into account the whole trajectory. Finally, we present numerical results for different examples of eBSDEs and forward utilities along with the associated investment strategies.

math.PR↗