Title: Modelling The Earth for Future Climate Risks

Abstract: Our planet's climate is changing, driving extreme weather events around the world, and leading to an uncertain future with numerous challenges. In order to identify these challenges and quantify future risk factors, we use complex computer modelling to predict the future state of the climate under various scenarios. From these model results we can see and try to quantify future risk events.

In this talk, I will introduce how we model the complex processes that make up the earth's climate, identify future risks and understand probabilities of those events. I will also discuss potential mitigation strategies that could affect our scenario predictions as well as touching on low-likelihood, high-impact possible events.

Title: A Consistent and Robust Test for Autocorrelated Jump Occurrences

Abstract: We develop a nonparametric test for the temporal dependence of jump occurrences in the population. The test is consistent against all pairwise serial dependence, and is robust to the jump activity level and the choice of sampling scheme. We establish asymptotic normality and local power property for a rich set of local alternatives, including both self-exciting and/or self-inhibitory jumps. Simulation study confirms the robustness of the test and reveals its competitive size and power performance over existing tests. In an empirical study on high-frequency stock returns, our procedure uncovers a wide array of autocorrelation profiles of jump occurrences for different stocks in different time periods.

Title: Berry-Esseen Bounds for Functionals of Independent Random Variables

Abstract: We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on a continuous-time integration by parts setting and discrete chaos expansions methods. Our approach improves on related results obtained in discrete-time integration by parts settings and applies to U-statistics satisfying the weak assumption of decomposability in the Hoeffding sense. It also yields Kolmogorov distance bounds instead of the Wasserstein bounds previously derived in the special case of degenerate U -statistics. 

Linear and quadratic functionals of arbitrary sequences of independent random variables are considered as particular cases, with new fourth moment bounds, and applications are given to Hoeffding decompositions, weighted U-statistics, quadratic forms, and random subgraph weighing. In the case of quadratic forms, our results recover and improve the bounds available in the literature, and apply to matrices with non-empty diagonals.

This is a joint work with Grzegorz Serafin, Wroclaw. 

Title: Time Series Quantile Regressions by using Random Forest

Abstract: We consider the estimation of quantiles for dependent data by using random forests. 

The quantile regression introduced by Koenker and Bassett (1978) has been discussed under time series setting by some paper such as QAR (Koenker and Xiao, 2004) or CAViaR (Engle and Manganelli, 2004). 

On the other hand, Quantile Regression Forests (QFR) is introduced under regression model by Meinshausen (2006). We discuss the QRF under time series setting.

Title: Optimal Relativities, Profitability, and Efficiency in a Modified Bonus-Malus System

Abstract: In the classical Bonus-Malus System (BMS) in automobile insurance, the premium for the next year is adjusted according to the policyholder's claim history (particularly frequency) in the previous year. Some variations of the classical BMS have been considered by taking more of the driver's claim experience into account to better assess an individual's risk. In this talk, we revisit a modified BMS which was briefly introduced in Lemaire (1995) and Pitrebois et al. (2003a). Specifically, such a BMS extends the number of Bonus-Malus (BM) levels due to an additional component in the transition rules representing the number of consecutive claim-free years. With the extended BM levels granting a more reasonable bonus to careful drivers, this paper investigates the transition rules more rigorously and provides the optimal BM relativities under various statistical model assumptions including the frequency random effect model and the dependent collective risk model. Also, numerical analysis of a real data set is provided to compare the classical BMS and our proposed BMS. Finally, some remarks regarding overall stationary premium and efficiency measures are provided. 

This is based on joint work with Ahn, Cheung, and Oh (funded by the Casualty Actuarial Society).