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Events - September 2020

Thursday, September 24, 2020 — 4:00 PM EDT

Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency

We consider spatially dependent functional data collected under a geostatistics setting, where spatial locations are irregular and random. The functional response is the sum of a spatially dependent functional effect and a spatially independent functional nugget effect. Observations on each function are made on discrete time points and contaminated with measurement errors. Under the assumption of spatial stationarity and isotropy, we propose a tensor product spline estimator for the spatio-temporal covariance function. When a coregionalization covariance structure is further assumed, we propose a new functional principal component analysis method that borrows information from neighboring functions. The proposed method also generates nonparametric estimators for the spatial covariance functions, which can be used for functional kriging. Under a unified framework for sparse and dense functional data, infill and increasing domain asymptotic paradigms, we develop the asymptotic convergence rates for the proposed estimators. Advantages of the proposed approach are demonstrated through simulation studies and two real data applications representing sparse
and dense functional data, respectively.

Please note: This talk will be hosted on Zoom. To join please click on the following link: Department seminar by Yehua Li

Meeting ID: 844 283 6948 

Passcode: 318995

Friday, September 18, 2020 — 10:30 AM EDT

De Finetti's optimal dividends problem with linearly bounded payment rates

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.

Please Note: This talk will be hosted on Webex. To join please the following link: Department Seminar by Jean-Francois Renaud

Thursday, September 17, 2020 — 4:00 PM EDT

A new framework for modeling sparse networks that makes sense (and can actually be fit!)

Latent position models are a versatile tool when working with network data. Applications include clustering entities, network visualization, and controlling for unobserved causal confounding. In traditional treatments of the latent position model, the nodes’ latent positions are viewed as independent and identically distributed random variables. This assumption implies that the average node degree grows linearly with the number of nodes in the network, making it inappropriate when the network is sparse. In the first part of this talk, I will propose an alternative assumption—that the latent positions are generated according to a Poisson point process—and show that it is compatible with various levels of network sparsity. I will also provide theory establishing that the nodes’ latent positions can be consistently estimated, provided that the network isn't too sparse.  In the second part of the talk, I will consider the computational challenge of fitting latent position models to large datasets. I will describe a new Markov chain Monte Carlo strategy—based on a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo—that is much more efficient than the standard Metropolis-within-Gibbs algorithm for inferring the latent positions. Throughout the talk, I will use an advice-sharing network of elementary school teachers within a school district as a running example.

Please note: This talk will be hosted on Webex. To join please click on the following link: Department seminar by Neil Spencer.

Friday, September 11, 2020 — 10:30 AM EDT

On the profitability of selfish blockchain mining under consideration of ruin


Mining blocks on a blockchain equipped with a proof of work consensus protocol is known to be resource-consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining, and is compensated by a capital gain when a block is discovered. In this talk we quantify the profitability of mining when the possible event of ruin is also taken into consideration. This is done by formulating a tractable stochastic model and using tools from actuarial ruin theory and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when he/she withholds blocks.  The obtained explicit expressions allow to analyze the sensitivity with respect to the different model ingredients and to identify conditions under which selfish mining is a strategic advantage. The talk is based on joint work with P.O. Goffard.

Please Note: This talk will be hosted on Webex.  To join please the following link: Department Seminar by Hansjoerg Albrecher

Thursday, September 10, 2020 — 4:00 PM EDT

Network Response Regression for Modeling Population of Networks with Covariates


Multiple-network data are fast emerging in recent years, where a separate network over a common set of nodes is measured for each individual subject, along with rich subject covariates information. Existing network analysis methods have primarily focused on modeling a single network, and are not directly applicable to multiple networks with subject covariates.

In this talk, we present a new network response regression model, where the observed networks are treated as matrix-valued responses, and the individual covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the parsimonious effects of subject covariates on the network through a sparse slope tensor. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating gradient descent algorithm. We establish the non-asymptotic error bound for the actual estimator from our optimization algorithm. Built upon this error bound, we derive the strong consistency for network community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through intensive simulations and two brain connectivity studies.

 

Join Zoom Meeting

Meeting ID: 844 283 6948
Passcode: 318995

Friday, September 4, 2020 — 10:30 AM to 11:30 AM EDT

Insurance Risk Analysis of Financial Networks


We conduct a quantitative risk analysis of non-core insurance business of selling financial products to protect financial firms  against investment losses due to a shock. To achieve the goal, we construct a static structural model composed of a network of firms who cross-hold each other, multiple primitive assets that are vulnerable to a shock, and an insurer who resides external to the network and speculates in selling protection to financial firms. Assume that each firm in the network is rational and able to decide how much protection to purchase to optimize its portfolio according to the mean-variance principle. As a result, the shock may impact the insurer but indirectly through the network, and thus both the network integration and the shock are risk factors of this non-core insurance business. Our study focuses on describing their interactive role in the insurance risk. Depending on the shock size, an increase in the network integration (which refers to the level of exposures of firms to each other) may help reduce the insurance risk, or drive the insurer to a more profitable position, or hinder the insurer from making profit.

Please Note: This talk will be given on Webex. Click here to join: Seminar by Qihe Tang

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