To split or not to split: capital allocation with convex risk measures

Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed.

Updated: 22/09/2011
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Views: 5,259

Risk measures and theories of choice

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003), whereas Yaari's (1987) dual theory of risk can be viewed as the source of the distortion premium principle (Denneberg (1990), Wang (1996).

Updated: 22/09/2011
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Views: 5,300

Froot and Stein revisited once again

Author(s):

Jens Nielsen

 et al.

In this paper we show that the economic intuition behind the paper of Froot and Stein (1998) is correct and that their result can be obtained when the market is reformulated in a discrete time setting.

Updated: 22/09/2011
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Views: 5,794

A mixing model for operational risk

Author(s):

Jens Nielsen

 et al.

External data can often be useful in improving estimation of operational risk loss distributions. This paper develops a systematic approach that incorporates external information into internal loss distribution modelling.

Updated: 22/09/2011
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Views: 5,543

Combining underreported internal and external data for operational risk measurement

Author(s):

Jens Nielsen

 et al.

This paper proposes a model for operational losses that improves the internal loss distribution modelling by combining internal and external operational risk data. It also considers the possibility that internal and external data have been collected with a different truncation threshold.

Updated: 22/09/2011
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Views: 5,834

Estimating multiplicative and additive hazard functions by Kernel methods

Author(s):

Jens Nielsen

 et al.

We propose new procedures for estimating the univariate quantities of interest in both additive and multiplicative nonparametric marker dependent hazard models.

Updated: 22/09/2011
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Views: 5,141

Non-parametric regression with a latent time series

In this paper we investigate a class of semi-parametric models for panel data sets where the cross-section and time dimensions are large.

Updated: 22/09/2011
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Views: 5,298

Multidimensional credibility with time effects: an application to commercial business lines

Author(s):

Jens Nielsen

 et al.

This article considers Danish insurance business lines for which the pricing methodology has been dramatically upgraded recently.

Updated: 22/09/2011
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Views: 5,450

Optimal management of an insurer's exposure in a competitive general insurance market

The qualitative behaviour of the optimal premium strategy is determined for an insurer in a finite and an infinite market using a deterministic general insurance model. The optimisation problem leads to a system of forward-backward differential equations obtained from Pontryagin's Maximum Principle. An analytical optimal premium strategy is also found using inverse methods when the price function is nonlinear.

Updated: 22/09/2011
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Views: 5,722