Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range

Physics-aware registration based auto-encoder for convection dominated PDEs

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by a large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Moreover, the realized latent variables are often hard to interpret. Therefore, many of these methods are often dismissed in the reduced order modeling of dynamical systems governed by the partial differential equations (PDEs). Accordingly, we propose an auto-encoder type nonlinear dimensionality reduction algorithm. The unsupervised learning problem trains a diffeomorphic spatio-temporal grid, that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.Comment: 10 pages, 6 figure

Diagnostic and prognostic relevance of microparticles in peripheral and uterine blood of patients with endometrial cancer

Objectives: Exosomes — microvesicles which are secreted by living cells — can be produced from different cell types and detected in various body fluids. They are the carriers of intercellular information which regulate tumor microenvironment and are considered to be involved in tumor progression and metastasis. Cancer cells can secrete more exosomes than healthy cells, and are expected to be potential tools for tumor diagnosis and treatment.Material and methods: In this report, we present the results of microparticle analysis in peripheral and uterine blood of patients with endometrial cancer. To the best of our knowledge, this study has been the first to report microvesicle status in peripheral and uterine blood samples. The aim of the study was to determine the amount of total (TF+), endothelial (CD144+) and monocytic (CD14+) microparticles. The counting of the selected microparticles in citrate plasma was performed using flow cytometry on the BD Canto II cytometer.Results: We found that the total amount of microparticles in cancer patients was much higher than in healthy controls. Moreover, microparticle count in uterine blood was higher than in peripheral blood of patients with endometrial cancer. Wealso demonstrated that the amount of microparticles correlates with the histologic grade and clinical stage of the tumor.Conclusions: The most interesting finding in this work was the high level of TF, CD144 and CD14 MPs in uterine blood samples. Thus we can consider the monocyte-macrophage-derived MPs as a candidate marker of endometrial cancer and maybe very critical part of the endometrial carcinogenesis