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Evaluating capital requirements as well as allocating total capital into various business units are becoming increasingly important part of the risk management process of a financial enterprise. In the allocation of capital, we consider the purpose of capital allocation within a company (individual, collective, or market-relative), the manner in which the… (More)

The Aumann–Shapley [Values of Non-atomic Games, Princeton University Press, Princeton] value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault [Coherent allocation of risk capital, J. Risk 4 (1) (2001) 1]. We obtain an explicit formula for the Aumann–Shapley value,… (More)

- Andreas Tsanakas, Evangelia Desli
- Risk analysis : an official publication of the…
- 2005

The theory and practice of risk measurement provides a point of intersection between risk management, economic theories of choice under risk, financial economics, and actuarial pricing theory. This article provides a review of these interrelationships, from the perspective of an insurance company seeking to price the risks that it underwrites. We examine… (More)

- Andreas Tsanakas, Pietro Millossovich
- Risk analysis : an official publication of the…
- 2016

In a quantitative model with uncertain inputs, the uncertainty of the output can be summarized by a risk measure. We propose a sensitivity analysis method based on derivatives of the output risk measure, in the direction of model inputs. This produces a global sensitivity measure, explicitly linking sensitivity and uncertainty analyses. We focus on the case… (More)

- Ruodu Wang, Valeria Bignozzi, Andreas Tsanakas
- SIAM J. Financial Math.
- 2015

Portfolio diversification, as quantified by a risk measure, is intrinsically linked with the potential for superadditivity that the risk measure displays. In this paper, we study the extent to which any risk measure can lead to superadditive risk assessments. For this purpose we introduce the novel notion of extreme-aggregation risk measures. For a… (More)

- R Gerrard, A Tsanakas
- Risk analysis : an official publication of the…
- 2011

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks… (More)

For solvency purposes insurance companies need to calculate so-called best-estimate reserves for outstanding loss liability cash flows and a corresponding risk margin for nonhedgeable insurance-technical risks in these cash flows. In actuarial practice, the calculation of the risk margin is often not based on a sound model but various simplified methods are… (More)

- Francesca Biagini, Rene Carmona, +31 authors Christoph Czichowsky
- 2015

- Andreas Tsanakas
- 2017

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… (More)

We use mean-variance hedging in discrete time in order to value an insurance liability. The prediction of the insurance liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected values until the liability is finally settled. We assume the existence of a tradeable derivative with binary pay-off… (More)

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