Change-point detection for expected shortfall in time series

Expected shortfall (ES) is a popular risk measure and plays an important role in risk and portfolio management. Recently, change-point detection of risk measures has been attracting much attention in finance. Based on the self-normalized CUSUM statistic in Fan, Glynn and Pelger (2018) and the Wild Binary Segmentation (WBS) algorithm in Fryzlewicz (2014), this paper proposes a variant WBS procedure to detect and estimate change points of ES in time series. The strengthened Schwarz information criterion is also introduced to determine the number of change points. Monte Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time series. An empirical application is given to illustrate the usefulness of our procedure.     

对中国形成世界制造中心进程的冷思考

改革开放以来，我国迅速成为制造业大国，但还远远不是制造业的世界中心。只有认清我国制造业存在的预期利润低、结构不合理、产业链的低端定位、边际效应递减、研究与开发费用不足以及教育结构对制造业的瓶颈效应等问题，并对症下药，才能将我国的制造业真正做大做强。     

THEORIES OF CHOICE UNDER IGNORANCE AND UNCERTAINTY

Abstract. In this paper, Knight's distinction between risk and uncertainty, and its significance for economic analysis are examined. The paper consists of a survey of some recent developments on the theory of choice under uncertainty and some applications of these theories to problems for which Bayesian Decision Theory has not proved entirely satisfactory. Two problems are examined in detail. The first is that of finance and insurance and the second is that of risktaking behaviour with special emphasis on lotteries.     

A Bayesian approach for more reliable tail risk forecasts

This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.     

Subjective recursive expected utility

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.Part of this research was conducted when Ozdenoren visited MEDS in Fall 2003. We thank Tapas Kundu, Costis Skiadas, Jean-Marc Tallon and Tan Wang for helpful discussions and also thank audiences at Koc University, Northwestern University, the CERMSEM conference “ Mathematical Models in Decision Theory” at Universite Paris I, and the FUR XI conference on foundations and applications of utility, risk and decision theory     

Medical insurance with rank-dependent utility

Summary. A well-known result in the medical insurance literature is that zero co-insurance is never second-best for insurance contracts subject to moral hazard. We replace the usual expected utility assumption with a version of the rank-dependent utility (RDU) model that has greater experimental support. When consumers exhibit such preferences, we show that zero co-insurance may in fact be optimal, especially for low-risk consumers. Indeed, it is even possible that the first-best and second-best contracts are identical. In this case, there is no “market failure”, despite the informational asymmetry. We argue that these RDU results are in better accord with the empirical evidence from US health insurance markets. Received: February 26, 2001; revised version: October 4, 2002 RID="*" ID="*"The authors would particularly like to thank Simon Grant, John Quiggin, Peter Wakker and an anonymous referee for valuable comments and suggestions on earlier drafts. The paper has also benefitted from the input of seminar audiences at The Australian National University, University of Auckland, University of Melbourne and University of Sydney. Ryan also gratefully acknowledges the financial support of the ARC, through Grant number A000000055. Correspondence to:R. Vaithianathan     

基于客流和消费水平随机变化的社区服务网点规模及盈利条件分析

基于影响服务网点利润的客流量和消费水平两个随机因素进行分析,运用概率论相关理论,给出了服务网点销售额和利润的概率分布,由此确定投资规模及盈利条件。     

More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model

Summary. This paper studies monotone risk aversion, the aversion to monotone, mean-preserving increase in risk (Quiggin [21]), in the Rank Dependent Expected Utility (RDEU) model. This model replaces expected utility by another functional, characterized by two functions, a utility function u in conjunction with a probability-perception function f. Monotone mean-preserving increases in risk are closely related to the notion of comparative dispersion introduced by Bickel and Lehmann [3,4] in Non-parametric Statistics. We present a characterization of the pairs (u,f) of monotone risk averse decision makers, based on an index of greediness G _u of the utility function u and an index of pessimism P _f of the probability perception function f: the decision maker is monotone risk averse if and only if . The index of greediness (non-concavity) of u is the supremum of taken over . The index of pessimism of f is the infimum of taken over 0 < v < 1. Thus, , with G _u = 1 iff u is concave. If then , i.e., f is majorized by the identity function. Since P _f = 1 for Expected Utility maximizers, forces u to be concave in this case; thus, the characterization of risk aversion as is a direct generalization from EU to RDEU. A novel element is that concavity of u is not necessary. In fact, u must be concave only if P _f = 1.Received: 10 April 2001, Revised: 18 November 2003, JEL Classification Numbers: D81. Correspondence to: Michéle CohenAlain Chateauneuf, Michéle Cohen, Isaac Meilijson: We are most grateful to Mark Machina, Peter Wakker and two anonymous referees for very helpful suggestions and comments.     

Diversification, convex preferences and non-empty core in the Choquet expected utility model

Summary. We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index. Received: July 27, 1999; revised version: November 7, 2000     

Revisiting Savage in a conditional world

Summary. I present an axiomatization of subjective expected utility and Bayesian updating in a conditional decision problem. This result improves our understanding of the Bayesian standard from two perspectives: 1) it uses a set of axioms which are weak and intuitive; 2) it provides a formal proof to results on the relation between dynamic consistency, expected utility and Bayesian updating which have never been explicitly proved in a fully subjective framework. Received: December 1, 2000; revised version: February 26, 2001