Friday, March 29, 2019 — 10:30 AM EDT

Background risk model and inference based on ranks of residuals

It is often easier to model the behaviour of a random vector by choosing the marginal distributions and the copula separately rather than using a classical multivariate distribution. Many copula families, including the classes of Archimedean and elliptical copulas, may be written as the survival copula of a random vector R(X,Y), where R is a strictly positive random variable independent of the random vector (X,Y). A unified framework is presented for studying the dependence structure underlying this stochastic representation, which is called the background risk model. However, in many applications, part of the dependence may be explained by observable external factors, which justifies the use of generalized linear models for the marginal distributions. In this case and under some conditions that will be discussed, the inference on the copula can be based on the ranks of suitable residuals.

Thursday, March 28, 2019 — 4:00 PM EDT

Excursion Probabilities and Geometric Properties of Multivariate Gaussian Random Fields

Excursion probabilities of Gaussian random fields have many applications in statistics (e.g., scanning statistic and control of false discovery rate (FDR)) and in other areas. The study of excursion probabilities has had a long history and is closely related to geometry of Gaussian random fields. In recent years, important developments have been made in both probability and statistics.

In this talk, we consider the excursion probabilities of bivariate Gaussian random fields with non-smooth (or fractal) sample functions and study their geometric properties and excursion probabilities. Important classes of multivariate Gaussian random fields are those stationary with Matérn cross-covariance functions [Gneiting, Kleiber, and Schlather (2010)] and operator fractional Brownian motions which are operator-self-similar with stationary increments.

Friday, March 15, 2019 — 10:30 AM EDT

Modeling Winning Streaks in Financial Markets & Sample Recycling Method for Nested Stochastics

Topic #1:

A new class of stochastic processes, termed sticky extrema processes, is proposed to model common phenomena of winning and losing streaks in financial markets including equity, commodity, foreign exchange, etc. Most stochastic process models for financial market data in the current literature focus on stylized facts such as fail tailedness relative to normality, volatility clustering, mean reversion, etc. However, none of existing financial models captures a frequently observable “extrema clustering" feature that most financial indices often report record high or low in concentrated periods of time. The lack of “extrema clustering" feature in a stochastic model for asset valuation can have a grave impact on the pricing and risk management of path-dependent financial derivatives. Especially those with payoffs dependent on optimal (maximum or minimum) underlying market values can be severely misestimated.

Topic #2:

Nested stochastic modeling has been on the rise in many fields of the financial industry. Nested stochastic models refer to stochastic models embedded inside other stochastic models. Examples can be found in principle-based reserving for long term insurance liabilities. Reserves and capitals for interest and market risk sensitive financial products are often determined by stochastic valuation. In the projection of cash flows, further simulations are necessary to evaluate risk management action, such as a hedging program, at each point of time. The computational demand grows exponentially with the layers of nested stochastic modeling and points of evaluation. Most of existing techniques to speed up nested simulation are based on curve fitting, which is to establish a functional relationship between inner loop estimator and economic scenarios and to replace inner loop simulations with the fitted curve. This work presents a non-conventional approach, termed sample recycling method, which is to run inner loop estimation for a small set of outer loop scenarios and find estimates under other outer loop scenarios by recycling inner loop paths. This new approach can be very efficient when curve fittings are difficult to achieve.

Thursday, March 14, 2019 — 4:00 PM EDT

A Unified Approach to Sparse Tweedie Modeling of Multi-Source Insurance Claim Data

Actuarial practitioners now have access to multiple sources of insurance data corresponding to various situations: multiple business lines, umbrella coverage, multiple hazards, and so on. Despite the wide use and simple nature of single-target approaches, modeling these types of data may benefit from a simultaneous approach. We propose a unified algorithm to perform sparse learning of such fused insurance data under the Tweedie (compound Poisson) model. By integrating ideas from multi-task sparse learning and sparse Tweedie modeling, our algorithm produces flexible regularization that balances predictor sparsity and between-sources sparsity. When applied to simulated and real data, our approach clearly outperforms single-target modeling in both prediction and selection accuracy, notably when the sources do not have exactly the same set of predictors. An efficient implementation of the proposed algorithm is provided in our R package MStweedie.

Friday, March 8, 2019 — 10:30 AM EST

Risk Aggregation: A General Approach via the Class of Generalized Gamma Convolutions

Risk aggregation is virtually everywhere in insurance applications. Indeed, in the vast majority of situations insurers are interested in the properties of the sums of the risks they are exposed to, rather than in the stand-alone risks per se. Unfortunately, the problem of formulating the probability distributions of the aforementioned sums is rather involved, and as a rule does not have an explicit solution. As a result, numerous methods to approximate the distributions of the sums have been proposed, with the moment matching approximations (MMAs) being arguably the most popular. The arsenal of the existing MMAs is quite impressive and contains such very simple methods as the normal and shifted-gamma approximations that, respectively, match the first two and three moments, only, as well as such much more intricate methods as the one based on the mixed Erlang distributions. Note however that in practice the sums of insurance risks can have numerous and just a few summands; in the latter case the normal

approximation is very questionable. Also, in practice the distributions of the stand-alone risks can be light-tailed or heavy-tailed; in the latter case moments of higher orders (e.g., second, etc.) may not exist, and so the approximation based on mixed Erlang distributions is of limited usefulness. In this talk I will reveal a refined MMA method for approximating the distributions of the sums of insurance risks. The method approximates the distributions of interest to any desired precision, works equally well for light and heavy-tailed distributions, and is reasonably fast irrespective of the number of the involved summands. (This is a joint work with Justin Miles and Alexey Kuznetsov, York University.)

Thursday, March 7, 2019 — 4:00 PM EST

Non-standard problems in statistical inference:Bartlett identity, boundary, identifiability issues

In this talk, I will cover a few ideas in tackling non-standard problems in statistical inference, including Bartlett identity, boundary and identifiability issues. I will show that these considerations are critical in model robustness, statistical power, and validity. I will also present implications of these ideas in addressing key challenges in biomedical research using massive healthcare data, in particular, electronic health records, drug/vaccine safety surveillance data. Case studies using University of Pennsylvania Biobank data will be provided.

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