On Haezendonck risk measures

We study the Haezendonck risk measure (introduced by [Haezendonck, J., Goovaerts, M., 1982. A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1, 41–53] and by [Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2003. A unified approach to generate risk measures. ASTIN Bulletin 33 (2), 173–191; Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2004. Some new classes of consistent risk measures. Insurance: Mathematics and Economics 34 (3), 505–516]) and prove its subadditivity. Since the Haezendonck risk measure is defined as an infimum of Orlicz premia, we investigate when the infimum is actually attained. We determine the corresponding generalized scenarios and show how its construction can be seen as a special case of the operation of inf-convolution of convex functionals.     

On fairness of systemic risk measures

Finance and Stochastics - In our previous paper “A unified approach to systemic risk measures via acceptance sets” (Mathematical Finance, 2018), we have introduced a general class of...     

On a class of law invariant convex risk measures

We consider the class of law invariant convex risk measures with robust representation r_h,p(X)=sup_fò₀¹ [AV@R_s(X)f(s)-f^p(s)h(s)] ds\rho_{h,p}(X)=\sup_{f}\int_{0}^{1} [AV@R_{s}(X)f(s)-f^{p}(s)h(s)]\,ds, where 1≤p<∞ and h is a positive and strictly decreasing function. The supremum is taken over the set of all Radon–Nikodym derivatives corresponding to the set of all probability measures on (0,1] which are absolutely continuous with respect to Lebesgue measure. We provide necessary and sufficient conditions for the position X such that ρ _h,p (X) is real-valued and the supremum is attained. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and compare them to the average value at risk.     

应分步实施消费型增值税

在东北三省进行增值税转型的试点刚刚开始,试点方案的优劣暂时难以辨明,笔者赞同实施消费型增值税,但对于新增机器设备和房屋建筑物等固定资产所含进项税金的抵扣方式有不同意见,考虑到对财政收入的影响,笔者建议采取分步抵扣法.     

Vector-valued coherent risk measures

We define (d,n)-coherent risk measures as set-valued maps from into satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from valued random portfolio to valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.Received: February 2004, Mathematics Subject Classification (2000): 91B30, 46E30JEL Classification: D81, G31     

Dynamic risk measures: Time consistency and risk measures from BMO martingales

Time consistency is a crucial property for dynamic risk measures. Making use of the dual representation for conditional risk measures, we characterize the time consistency by a cocycle condition for the minimal penalty function. Taking advantage of this cocycle condition, we introduce a new methodology for the construction of time-consistent dynamic risk measures. Starting with BMO martingales, we provide new classes of time-consistent dynamic risk measures. These families generalize those obtained from backward stochastic differential equations. Quite importantly, starting with right-continuous BMO martingales, this construction naturally leads to paths with jumps.      

Inf-convolution of risk measures and optimal risk transfer

We develop a methodology for optimal design of financial instruments aimed to hedge some forms of risk that is not traded on financial markets. The idea is to minimize the risk of the issuer under the constraint imposed by a buyer who enters the transaction if and only if her risk level remains below a given threshold. Both agents have also the opportunity to invest all their residual wealth on financial markets, but with different access to financial investments. The problem is reduced to a unique inf-convolution problem involving a transformation of the initial risk measures.Received: December 2004, Mathematics Subject Classification (2000): 60G35, 91B28, 91B30, 46N10JEL Classification: C61, D81, G13, G22     

Putting order in risk measures

This paper introduces a set of axioms that define convex risk measures. Duality theory provides the representation theorem for these measures and the link with pricing rules.     

On the necessity of solving the free rider problem in takeover bids

Previous analysis of the free rider problem in takeover bids has concluded that complex takeover strategies, nonprice taking behavior, taxes, or exogenous exclusion of minority shareholders are necessary for the bidder to profit from a takeover bid. In contrast, in this study, costs of disclosure and the fungible nature of the bidder's information mitigates the detrimental consequences of the free rider problem. The absence of the free rider problem in takeover bids has important implications for optimal bidding strategies, the interpretation of mechanisms posed as solutions to the free rider problem, and the analysis of regulation of takeover activity.     

On dynamic spectral risk measures,a limit theorem and optimal portfolio allocation

In this paper, we propose the notion of continuous-time dynamic spectral risk measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk measures in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk measures, which are obtained by iterating a given spectral risk measure (such as expected shortfall) along a given time-grid. Specifically, we demonstrate that any DSR arises in the limit of a sequence of such iterated spectral risk measures driven by lattice random walks, under suitable scaling and vanishing temporal and spatial mesh sizes. To illustrate its use in financial optimisation problems, we analyse a dynamic portfolio optimisation problem under a DSR.     

利用非法律措施化解担保业务风险

非法律措施与法律诉讼是担保业务风险化解和风险处置不同阶段采取的相应措施,充分运用非法律措施,化解风险,维系有关各方良好的可持续发展关系,具有十分重要的积极意义     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Update rules for convex risk measures

In the first part of the paper we investigate the properties that describe the intertemporal structure of dynamic convex risk measures. The usual backward approach to dynamic risk assessment leads to strong and weak versions of time consistency. As an alternative, we introduce a forward approach of consecutivity. In the second part we discuss the problem of how to update a convex risk measure when new information arrives. We analyse to what extent the above properties are appropriate update criteria.     

Systemic risk measures and regulatory challenges

This paper discusses different definitions of systemic risk and identifies the challenges, which regulators face in addressing this phenomenon. We conducted a systematic literature review of 4859 abstracts to categorize the various methodologies developed to measure systemic risk. In total, 60 systemic risk measures proposed post-2000 have been critically appraised to inform academics and regulators of their practical applications and model vulnerabilities. This review suggests that most of these methods focus on individual financial institutions rather than on system stability. Those methodologies directly reflect the current regulations, which aim to ensure individual institutions’ soundness. As macro-prudential regulation evolves, policy-makers face the issues of understanding contagion and how regulations should be implemented. This paper also discusses new systemic risk and regulatory challenges resulting from the current COVID-19 pandemic.