Weekly seminars: 2020
DecemberDec 10: Liyuan Lin (University of Waterloo)
Title: Sum of standard uniform random variables
Speaker: Liyuan Lin (PhD Candidate, University of Waterloo)
Time: 9:00am-10:00am EST, Dec 10 (Thu)
Location: Online via Zoom
Abstract: In this paper, we analyse the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are obtained for two distinct cases. In the case of dimension two, we obtain four partial characterization results. For dimension greater than or equal to three, we obtain a full characterization of the set of aggregate distributions, which is the first complete characterization result of this type in the literature for any choice of continuous marginal distributions.
Dec 3: Dr. Xia Han (University of Waterloo)
Title: Stochastic Stackelberg differential reinsurance games under time-inconsistent mean-variance framework
Speaker: Xia Han (Postdoc Fellow, University of Waterloo)
Time: 9:00am-10:00am EST, Dec 3 (Thu)
Location: Online via Zoom
Abstract: We study optimal reinsurance in the framework of stochastic Stackelberg differential game, in which an insurer and a reinsurer are the two players, and more specifically are considered as the follower and the leader of the Stackelberg game, respectively. An optimal reinsurance policy is determined by the Stackelberg equilibrium of the game, consisting of an optimal reinsurance strategy chosen by the insurer and an optimal reinsurance premium strategy by the reinsurer. Both the insurer and the reinsurer aim to maximize their respective mean–variance cost functionals. To overcome the time- inconsistency issue in the game, we formulate the optimization problem of each player as an embedded game and solve it via a corresponding extended Hamilton–Jacobi–Bellman equation. It is found that the Stackelberg equilibrium can be achieved by the pair of a variance reinsurance premium principle and a proportional reinsurance treaty, or that of an expected value reinsurance premium principle and an excess-of-loss reinsurance treaty.
November
Nov 26: Qinyu Wu (University of Science and Technology of China)
Title: Generalized Optimized Certainty Equivalent
Speaker: Qinyu Wu (PhD Candidate, University of Science and Technology of China)
Time: 9:00am-10:00am EST, Nov 26 (Thu)
Location: Online via Zoom
Abstract: In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on ϕ-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of RDU-based shortfall risk measure proposed by Mao and Cai (2018) is also presented.
Nov 19: Zhanyi Jiao (University of Waterloo)
Title: Peer-to-peer multi-risk insurance and mutual aid
Speaker: Zhanyi Jiao (PhD Candidate, University of Waterloo)
Time: 9:00am-10:00am EST, Nov 19 (Thu)
Location: Online via Zoom
Abstract: Peer-to-peer (P2P) insurance is a decentralized network in which participants pool their resources together to compensate those who suffer losses. Despite the fast-changing landscape in this field, there has been no previous academic literature on the theoretical underpinning of P2P insurance. This paper presents the first effort to build the framework for the design and engineering of mutual aid and P2P insurance. Most of existing business models are developed to insure against a particular risk. This paper presents a variety of P2P insurance/mutual aid models that facilitate the exchange of multiple risks and enable peers with different needs to financially support each other in a transparent and fair way.
Nov 12: Prof. Ricardas Zitikis (Western University)
Title: Detecting systematic risks affecting systems when genuine inputs are stationary time series
Speaker: Ricardas Zitikis (Professor, Western University)
Time: 9:00am-10:00am EST, Nov 12 (Thu)
Location: Online via Zoom
Abstract: We develop a systematic-risk detection method when genuine inputs into the system originate from a large class of stationary random sequences, thus enabling the use of the method in a variety of applications. To show how the method works on data, and how to interpret results and make appropriate decisions, we illustrate the method when genuine inputs are ARMA time series and systematic risks (e.g., measurement errors) are sequences of iid random variables. (This is a joint work with Ning Sun and Chen Yang.)
Nov 5: Yuyu Chen (University of Waterloo)
Title: Pareto-optimal insurance contracts with premium budget and minimum charge constraints
Speaker: Yuyu Chen (PhD Candidate, University of Waterloo)
Time: 9:00am-10:00am EST, Nov 5 (Thu)
Location: Online via Zoom
Abstract: In view of the fact that minimum charge and premium budget constraints are natural economic considerations in any risk-transfer between the insurance buyer and seller, the optimal insurance contract design problem is studied in terms of Pareto optimality with imposing these practical constraints. Pareto optimal insurance contracts, with indemnity schedule and premium payment, are solved in the cases when the risk preferences of the buyer and seller are given by Value-at-Risk or Tail Value-at-Risk.
October
Oct 29: Yang Liu (Tsinghua University)
Title: A classification approach to general S-shaped utility optimization with principals' constraints
Speaker: Yang Liu (PhD Candidate, Tsinghua University)
Time: 10:00am-11:00am EST, Oct 29 (Thu)
Location: Online via Zoom
Abstract: We study a problem in the principal-agent model of two general S-shaped utilities without explicit expressions, where the two parties have different reference points. The problem is featured with a principal's participating incentive compatible constraint, which particularly stands in the context of asset management with motivation to safeguard the benefit of the principal. After a thorough investigation, it turns out to be a complicated double S-shaped utility optimization problem. We propose a new classification approach to study the optimal final asset allocation. First, it is classified into two cases: (a) One-side-loss Case in which either both parties suffer liquidation, or one gains and the other loses, or both make profit; (b) Option Case in which either both parties suffer liquidation or both make profit. Further, we demonstrate an asymptotic classification of the optimal asset allocation that the single utility maximization of the principal is the limit of the Option Case, while that of the agent is the limit of the One-side-loss Case. More importantly, we find a division reservation utility which the optimal asset allocation belongs to the Option Case beyond and to the One-side-loss Case below. Thus, the key factor resulting in different risk choices is the size of the reservation utility. As an application, we numerically visualize these results with a specific participating contract, which illustrates some novel mechanisms in asset management.
Oct 22: Mingren Yin (University of Waterloo)
Title: Worst-case Risk Measures and Robust Portfolio Optimization
Speaker: Mingren Yin (PhD Candidate, University of Waterloo)
Time: 10:00am-11:00am EST, Oct 22 (Thu)
Location: Online via Zoom
Abstract: Classical formulations of the portfolio optimization problem, such as mean-variance or Value-at-Risk (VaR) approaches, can result in a portfolio extremely sensitive to errors in the data, such as mean and covariance matrix of the returns. These two papers instead assumed the distribution of returns is partially known and considered the problem of computing the worst-case VaR and the worst-case CVaR, respectively, with respect to several types of model uncertainties. The both papers showed the problems can be converted into convex problems and hence are tractable.
Oct 15: Qiuqi Wang (University of Waterloo)
Title: Optimizing Distortion Riskmetrics with Distributional Uncertainty
Speaker: Qiuqi Wang (PhD Candidate, University of Waterloo)
Time: 10:00am-11:00am EST, Oct 15 (Thu)
Location: Online via Zoom
Abstract: Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not necessarily monotone or convex. One of our central findings is a unifying result which allows us to freely transform the optimization of a non-convex distortion riskmetric to that of a convex one, giving rise to great tractability in many practical problems. Key to the main unifying equivalence result, we introduce the notion of closedness under concentration for the set of plausible distributions. Our result includes many special cases that are well studied in the optimization literature, including but not limited to optimizing probability, Value-at-Risk, Expected Shortfall, and Yaari's dual utility under various forms of distributional uncertainty. We illustrate our theoretical results via applications to portfolio optimization, optimization under moment constraints, and preference robust optimization.
July
Jul 30: Prof. Silvana Pesenti (University of Toronto)
Title: Portfolio Optimisation within a Wasserstein Ball
Speaker: Silvana Pesenti (Assistant Professor, University of Toronto)
Time: 10:00am-11:00am, Jul 30 (Thu)
Location: Online via Zoom
Abstract: We consider the problem of active portfolio management where a loss-averse and/or risk-seeking investor aims to outperform a benchmark strategy's risk profile while staying ``close'' to the benchmark. Specifically, an investor considers alternative strategies whose (a) cost does not exceed that of the benchmark's, (b) whose terminal wealth and that of the benchmark's is comonotonic, and (c) whose terminal wealth lies within a Wasserstein ball around the benchmark's. The investor's personal risk profile is modelled by minimising a distortion risk measure. We prove that the optimal dynamic strategy exists and is unique, and provide a characterisation of the optimal strategy through the notion of isotonic projections. Moreover, we illustrate how investors with different risk preferences invest using the Tail Value-at-Risk and inverse S-shaped risk measures as examples.
Jul 23: Prof. Yunran Wei (Northern Illinois University)
Title: Elicitation Complexity of Statistical Properties
Speaker: Yunran Wei (Assistant Professor, Northern Illinois University)
Time: 10:00pm-11:00pm, Jul 23 (Thu)
Location: Online via Zoom
Jul 16: Takaaki Koike (University of Waterloo)
Title: Estimation and Comparison of Correlation-based Measures of Concordance
Speaker: Takaaki Koike (PhD Candidate, University of Waterloo)
Time: 10:00am-11:00am, Jul 16 (Thu)
Location: Online via Zoom
Abstract: We address the problem of estimating and comparing transformed rank correlation coefficients defined as Pearson’s linear correlation between two random variables transformed by a so-called concordance-inducing function. The class of transformed rank correlations includes Spearman’s rho, Blomqvist’s beta and van der Waerden’s coefficient as special cases by taking uniform, Bernoulli and normal distributions as concordance-inducing functions, respectively. We propose a novel framework for comparing transformed rank correlations in terms of the asymptotic variance of their canonical estimators. A general criterion derived from this framework is that concordance-inducing functions with smaller variances of squared random variables are more preferable. In particular, we show that Blomqvist’s beta attains the optimal asymptotic variance and Spearman’s rho outperforms van der Waerden’s coefficient. We also find that the optimal bounds of the asymptotic variance are attained by Kendall’s tau.
Jul 9: Dr. Xin Zang (Peking University)
Title: Joint Mix Copulas
Speaker: Dr. Xin Zang (Postdoc Fellow, Peking University)
Time: 10:00am-11:00am, Jul 9 (Thu)
Location: Online via Zoom
Abstract: In this paper, we study the joint mixability of symmetric distributions from a common location-scale family with characteristic generator in $\Phi_{2}$, which is the set of generators of 2-dimensional spherical distributions. First, we verify the equivalence of univariate unimodal-symmetric distributions and location-scale family with a characteristic generator of 3-dimensional spherical distributions. Second, we introduce some methodologies to construct joint mix copulas with margins from a common location-scale family, including the so-called recursive method and geometric method. Via our method, we can construct a large family of joint mix copulas with sufficient flexibility. Third, we investigate the simulation of joint mix distributions via the related copulas and provide some numerical illustrations. We partially give an answer to the Open Problems 8 and 9 in Wang (2015).
Jul 3: Prof. Mario Wüthrich (ETH Zurich)
Title: Nagging Predictor
Speaker: Mario Wüthrich (Professor, ETH Zurich)
Time: 11:00am-12:00am, Jul 3 (Fri)
Location: Online via Zoom
Abstract: We define the nagging predictor, which, instead of using bootstrapping to produce a series of i.i.d. predictors, exploits the randomness of neural network calibrations to provide a more stable and accurate predictor than is available from a single neural network run. Convergence results for such predictors can be proved, and we illustrate speed of convergence and improvement in prediction accuracy on a real car insurance data set.
June
Jun 26: Dr. Tolulope Fadina (University of Waterloo)
Title: Non-classical affine processes and their applications
Speaker: Tolulope Fadina (Postdoc Fellow, University of Waterloo)
Time: 9:00pm-10:00pm, Jun 26 (Fri)
Location: Online via Zoom
Abstract: This talk is based on two different frameworks that capture uncertainty in the financial market, especially in the interest rate market. First, we discuss affine processes under Knightian uncertainty where the parameters describing the dynamics of affine processes are assumed to lie in a confidence interval. Secondly, we assume the parameters of the process are driven by a Markov chain where the state represents different stages of an economy. As an example, we will talk about the corresponding Markov exponential-affine pricing formulas under Vasciek model in both frameworks.
Jun 19: Prof. Andreas Tsanakas (Cass Business School)
Title: Discrimination-free Insurance Pricing
Speaker: Andreas Tsanakas (Professor, Cass Business School, City University London)
Time: 11:00am-12:00am, Jun 19 (Fri)
Location: Online via Zoom
Abstract: We consider the following question: given information on individual policyholder characteristics, how can we ensure that insurance prices do not discriminate with respect to protected characteristics, such as gender? We address the issues of direct and indirect discrimination, the latter meaning that protected characteristics are implicitly learned (“proxied”) from non-protected ones. We provide mathematical definitions for direct and indirect discrimination and introduce a simple formula for discrimination-free pricing, which avoids both direct and indirect discrimination. This formula works in any statistical model. We demonstrate its application on a health insurance example, using a generalized linear model and a neural network regression model. An important conclusion is that discrimination-free pricing in general requires collection of policyholders’ discriminatory characteristics, posing potential challenges in relation to policyholder’s privacy concerns. Moving towards application of this approach in practice raises further questions, which I aim to discuss in the seminar. This is a joint work with M. Lindholm, R. Richman, M.V. Wuethrich.
Jun 12: Yuyu Chen (University of Waterloo)
Title: Ordering and Inequalities of Mixtures on Risk Aggregation
Speaker: Yuyu Chen (PhD Candidate, University of Waterloo)
Time: 9:00pm-10:00pm, Jun 12 (Fri)
Location: Online via Zoom
Abstract: In this paper we first investigate the ordering relationship between aggregation sets where the marginal risks from different sets are related by some simple operations, such as distribution-mixture or quantile-mixture defined by doubly stochastic matrices. It turns out that the aggregation set after operating a distribution-mixture becomes larger for general marginal distributions. However, the aggregation sets are not comparable under quantile-mixture operations in general. Our results on orders of aggregation sets imply that distribution-mixture operations on marginal risks can increase the worst-case values of risk measures for general marginal risks and general law-invariant risk measures. If all marginal distributions have decreasing densities, we show that quantile-mixture operations can produce a larger worst-case value of a specific regulatory risk measure, Value-at-Risk (VaR). We particularly focus on the worst-case values of risk measure for Pareto marginal distributions to obtain more specific inequalities related to the simple operations. Our results can be used to compare the the worst-case values of risk measures on two risk aggregations where no stochastic dominance exists between them. Numerical studies are conducted to illustrate our findings on inequalities for the worst-case values of VaR.
June 5: Mingren Yin (University of Waterloo)
Title: Risk measures based on behavioural economics theory
Speaker: Mingren Yin (PhD Candidate, University of Waterloo)
Time: 9:00pm-10:00pm, Jun 5 (Fri)
Location: Online via Zoom
May
May 29: Liyuan Lin (Central University of Finance and Economics)
Title: Self-consistency, subjective pricing, and a theory of credit rating
Speaker: Liyuan Lin (Graduate Student, Central University of Finance and Economics & University of Waterloo)
Time: 9:00pm-10:00pm, May 29 (Fri)
Location: Online via Zoom
May 24: Dr. Xia Han (Nanjing Normal University)
Title: Minimizing the probability of absolute ruin under ambiguity aversion
Speaker: Xia Han (PhD, Nanjing Normal University)
Time: 9:00pm-10:00pm, May 24 (Sun)
Location: Online via Zoom
May 15: Dr. Peng Liu (University of Waterloo)
Title: Functions operating on multivariate distributions
Speaker: Peng Liu (Postdoc Fellow, University of Waterloo)
Time: 9:00pm-10:00pm, May 15 (Fri)
Location: Online via Zoom
May 8: Prof. Xing Wang (Illinois State University)
Title: Extreme and inference for tail-Gini functionals with applications in tail risk management
Speaker: Xing Wang (Assistant Professor, Illinois State University)
Time: Fri, 9:00pm-10:00pm, May 8 (Fri)
Location: Online via Zoom
May 1: Qiuqi Wang (University of Waterloo)
Title: Risk quadrangles
Speaker: Qiuqi Wang (PhD Candidate, University of Waterloo)
Time: 9:00pm-10:00pm, May 1 (Fri)
Location: Online via Zoom
April
Apr 26: Yang Liu (Tsinghua University)
Title: Convolution bounds on quantile aggregation
Speaker: Yang Liu (PhD Candidate, Tsinghua University & University of Waterloo)
Time: 9:00pm-10:00pm, Apr 26 (Sun)
Location: Online via Zoom
March
Mar 12: Liyuan Lin (Central University of Finance and Economics)
Title: An axiomatic foundation of the Expected Shortfall
Speaker: Liyuan Lin (Graduate Student, Central University of Finance and Economics & University of Waterloo)
Time: 3:00pm-4:00pm, Mar 12 (Thu)
Location: Online via Zoom
Mar 5: Yang Liu (Tsinghua University)
Title: Bounds on quantile aggregation
Speaker: Yang Liu (PhD Candidate, Tsinghua University & University of Waterloo)
Time: 3:00pm-4:00pm, Mar 5 (Thu)
Location: M3-3001, University of Waterloo
February
Feb 25: Dr. Mengyi Xu (UNSW Business School)
Title: Retirement planning with systematic disability and mortality risk
Speaker: Mengyi Xu (Postdoc Fellow, UNSW Business School)
Time: 3:00pm-4:00pm, Feb 25 (Tue)
Location: M3-3001, University of Waterloo
Feb 13: Dr. Peng Liu (University of Waterloo)
Title: Is the inf-convolution of law-invariant preferences law-invariant?
Speaker: Peng Liu (Postdoc Fellow, University of Waterloo)
Time: 3:00pm-4:00pm, Feb 13 (Thu)
Location: M3-3001, University of Waterloo
Feb 6: Yuyu Chen (University of Waterloo)
Title: Trade-off between anytime- and sometime-safe methods for merging p-values
Speaker: Yuyu Chen (PhD Candidate, University of Waterloo)
Time: 4:00pm-5:00pm, Feb (Thu)
Location: M3-3001, University of Waterloo
January
Jan 30: Dr. Xiaole Xue (University of Waterloo)
Title: Minimax pricing and Choquet pricing
Speaker: Xiaole Xue (Postdoc Fellow, University of Waterloo)
Time: 3:00pm-4:00pm, Jan 30 (Thu)
Location: M3-3001, University of Waterloo
Jan 23: Mingren Yin (University of Waterloo)
Title: Risk measures derived from a regulator’s perspective on the regulatory capital requirements for insurers
Speaker: Mingren Yin (PhD Candidate, University of Waterloo)
3:00pm-4:00pm, Jan 23 (Thu)
M3-3001, University of Waterloo
Jan 16: Qiuqi Wang (University of Waterloo)
Title: Optimizing distortion riskmetrics with distributional uncertainty
Speaker: Qiuqi Wang (PhD Candidate, University of Waterloo)
Time: 3:00pm-4:00pm, Jan 16 (Thu)
Location: M3-4206, University of Waterloo
Jan 9: Yang Liu (Tsinghua University)
Title: A method to check whether an n-tuple of distributions with two-step densities is JM
Speaker: Yang Liu (PhD Candidate, Tsinghua University & University of Waterloo)
Time: 3:00pm-4:00pm, Jan 9 (Thu)
Location: M3-3001, University of Waterloo
Jan 5: Prof. Yunran Wei (Northern Illinois University)
Title: Risk management with non-convex and non-monotone preferences
Speaker: Yunran Wei (Assistant Professor, Northern Illinois University)
Time: 3:00pm-4:00pm, Jan 3 (Fri)
Location: M3-3001, University of Waterloo
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