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Real-valued conditional convex risk measures in Lp(ℱ, R)

Treviño-Aguilar Erick (2011)

ESAIM: Proceedings

The numerical representation of convex risk measures beyond essentially bounded financial positions is an important topic which has been the theme of recent literature. In other direction, it has been discussed the assessment of essentially bounded risks taking explicitly new information into account, i.e., conditional convex risk measures. In this paper we combine these two lines of research. We discuss the numerical representation of conditional...

Reinsurance-a new approach

Adam Paszkiewicz, Jakub Olejnik (2010)

Banach Center Publications

We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.

Risk aversion, prudence and mixed optimal saving models

Irina Georgescu (2014)

Kybernetika

The paper studies risk aversion and prudence of an agent in the face of a risk situation with two parameters, one described by a fuzzy number, the other described by a fuzzy variable. The first contribution of the paper is the characterization of risk aversion and prudence in mixed models by conditions on the concavity and the convexity of the agent's utility function and its partial derivatives. The second contribution is the building of mixed models of optimal saving and their connection with...

Risk measures versus ruin theory for the calculation of solvency capital for long-term life insurances

Pierre Devolder, Adrien Lebègue (2016)

Dependence Modeling

The purpose of this paper is twofold. First we consider a ruin theory approach along with risk measures in order to determine the solvency capital of long-term guarantees such as life insurances or pension products. Secondly, for such products,we challenge the definition of the Solvency Capital Requirement (SCR) under the Solvency II (SII) regulatory framework based on a yearly viewpoint. Several methods for the calculation of the solvency capital are presented. We start our study with risk measures...

Risk minimization in the model with transaction costs

Michał Motoczyński (2003)

Applicationes Mathematicae

The problem of hedging a contingent claim with minimization of quadratic risk is studied. Existence of an optimal strategy for the model with proportional transaction cost and nondelayed observation is shown.

Risk objectives in two-stage stochastic programming models

Jitka Dupačová (2008)

Kybernetika

In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and comment on their properties. It turns out that polyhedral risk functionals introduced in Eichorn and Römisch...

Robustness regions for measures of risk aggregation

Silvana M. Pesenti, Pietro Millossovich, Andreas Tsanakas (2016)

Dependence Modeling

One of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in...

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