Risk measurement in the presence of background risk

Abstract

A distortion-type risk measure is constructed, which evaluates the risk of any uncertain position in the context of a portfolio that contains that position and a fixed background risk. The risk measure can also be used to assess the performance of individual risks within a portfolio, allowing for the portfolio's re-balancing, an area where standard capital allocation methods fail. It is shown that the properties of the risk measure depart from those of coherent distortion measures. In particular, it is shown that the presence of background risk makes risk measurement sensitive to the scale and aggregation of risk. The case of risks following elliptical distributions is examined in more detail and precise characterisations of the risk measure's aggregation properties are obtained.

Loss reserving using loss aversion functions

“…The risk measure (1) appears in various guises -see for example the recent articles Tsanakas (2008) and Furman and Zitikis (2008) which point to the relationship of (1) to distortion operators in the insurance premium literature introduced by Denneberg (1990) and Wang (1996). Our treatment unifies and extends the existing literature.…”

“…The existing literature suffers from limited cross referencing and attribution even though approaches are closely related. For example expressions in the works of Wang (1995), Wang (1996), Wirch and Hardy (1999), Acerbi (2001) Acerbi (2002) and the recent works Tsanakas (2008)) and Furman and Zitikis (2008)) are weighted premiums in the sense of (1). Other close connections of (1) to suggestions appearing elsewhere in the literature are displayed in the sections below.…”

Optimal two-stage pricing strategies from the seller’s perspective under the uncertainty of buyer’s decisions

“…There are two major classes of such models: additive and multiplicative. For applications and discussions of additive models in Economic Theory, we refer to Gollier and Pratt (1996) and references therein, and to problems in Actuarial Science, we refer to Landsman (2005, 2010); Tsanakas (2008), and references therein. Our current research is essentially based on the multiplicative model, which has been extensively explored and utilized in the literature (see, e.g., Tsetlin and Winkler 2005;Franke et al 2006Franke et al , 2011Asimit et al 2016; references therein).…”

Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-Ii Model

“…In the actuarial, finance, and economic literature (cf., e.g., Finkelshtain et al [22], Franke et al [23,24], Nachman [25], Pratt [26], Tsanakas [27], and references therein), background risk has been modeled in a number of ways, such as additive, multiplicative, or more complex one that couples stand-alone risks/losses with the background risk. We also learn from these works that it is not easy to decide on the form of a coupling function, say h, that couples (unobservable) stand-alone risks ξ 1 , .…”