Capital Allocation for Portfolios with Non-Linear Risk Aggregation

32 Pages Posted: 21 May 2016 Last revised: 16 Nov 2016

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Andreas Tsanakas

City University London - Cass Business School

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: November 14, 2016

Abstract

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by L'evy processes, capturing the non-linear aggregation of insurance risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearized game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann-Shapley allocation, does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche's (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit.

Keywords: Capital allocation, Euler rule, fuzzy core, Aumann-Shapley value, risk measures

Suggested Citation

Boonen, Tim J. and Tsanakas, Andreas and Wuthrich, Mario V., Capital Allocation for Portfolios with Non-Linear Risk Aggregation (November 14, 2016). Insurance: Mathematics and Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2782033 or http://dx.doi.org/10.2139/ssrn.2782033

Tim J. Boonen

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profiel/b/o/t.j.boonen/t.j.boonen.html

Andreas Tsanakas (Contact Author)

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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