Thursday, April 25, 2019 — 4:00 PM EDT
Damir Filipovic

A Machine Learning Approach to Portfolio Risk Management

Risk measurement, valuation and hedging form an integral task in portfolio risk management for insurance companies and other financial institutions. Portfolio risk arises because the values of constituent assets and liabilities change over time in response to changes in the underlying risk factors. The quantification of this risk requires modeling the dynamic portfolio value process. This boils down to compute conditional expectations of future cash flows over long time horizons, e.g., up to 40 years and beyond, which is computationally challenging. 

This lecture presents a framework for dynamic portfolio risk management in discrete time building on machine learning theory. We learn the replicating martingale of the portfolio from a finite sample of its terminal cumulative cash flow. The learned replicating martingale is in closed form thanks to a suitable choice of the reproducing kernel Hilbert space. We develop an asymptotic theory and prove
convergence and a central limit theorem. We also derive finite sample error bounds and concentration inequalities. As application we compute the value at risk and expected shortfall of the one-year loss of some stylized portfolios.

Thursday, April 25, 2019 — 9:00 AM to Friday, April 26, 2019 — 5:00 PM EDT
Generic Pink Graph

The first Waterloo Conference in Statistics, Actuarial Science, and Finance (WATSAF1). 

Thursday, April 18, 2019 — 2:30 PM EDT

Regional-level genetic association testing under genomic partitioning adapted to local linkage disequilibrium

Motivated by characterizations of genomic architecture where multiple-variant analysis can uncover novel associations missed by single-variant analysis, we consider computationally efficient regression-based testing methods for regional genomic discovery, including genomic partitioning, that are feasible for genome-wide processing. To address the challenging question of how to specify appropriate regional units, we apply a novel haplotype block detection algorithm that uses interval graph modeling to cluster correlated variants and partition the genome into a large number of non-overlapping and quasi-independent linkage disequilibrium block regions. Within each block, we specify multiple-variant global test statistics with reduced dimension that maybe subject to multi-level testing. I will discuss some of the theoretical and practical issues we face in applications to quantitative trait and disease status analyses using dense genotyping/imputation genome-wide association study data.

Tuesday, April 9, 2019 — 4:00 AM EDT

Convergence to the Mean Field Game Limit: A Case Study

Friday, April 5, 2019 — 10:30 AM EDT

Conditional Optimal Stopping: A Time-Inconsistent Optimization

Thursday, April 4, 2019 — 4:00 PM EDT

Estimation methods to address correlated errors in time-to-event outcomes and exposures

Electronic health records (EHR) data are increasingly used in medical research, but EHR data, which typically are not collected to support research, are often subject to measurement error. These errors, if not addressed, can bias results in association analyses. Methodology to address covariate measurement error has been well developed; however, methods to address errors in time-to-event outcomes are relatively underdeveloped. We will consider methods to address errors in both the covariate and time-to-event outcome that are potentially correlated. We develop an extension to the popular regression calibration method for this setting. Regression calibration has been shown to perform well for settings with covariate measurement error (Prentice, 1982; Shaw and Prentice, 2012), but it is known that this method is generally biased for nonlinear regression models, such as the Cox model for time-to-event outcomes. Thus, we additionally propose raking estimators, which will be unbiased when an unbiased estimating equation is available on a validation subset. Raking is a standard method in survey sampling that makes use of auxiliary information on the population to improve upon the simple Horvitz-Thompson estimator applied to a subset of data (e.g. the validation subset). We demonstrate through numerical studies that raking can improve upon the regression calibration estimators in certain settings with failure-time data. We will discuss the choice of the auxiliary variable and aspects of the underlying estimation problem that affect the degree of improvement that the raking estimator will have over the simpler, biased regression calibration approach. Detailed simulation studies are presented to examine the relative performance of the proposed estimators under varying levels of signal, covariance, and censoring. We further illustrate the methods with an analysis of observational EHR data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

Wednesday, April 3, 2019 — 4:00 PM EDT

Causal Inference for Complex Observational Data

Observational data often have issues which present challenges for the data analyst.  The treatment status or exposure of interest is often not assigned randomly.  Data are sometimes missing not at random (MNAR) which can lead to sample selection bias.  And many statistical models for these data must account for unobserved confounding.  This talk will demonstrate how to use standard maximum likelihood estimation to fit extended regression models (ERMs) that deal with all of these common issues alone or simultaneously.

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