scholarly journals Capital Allocation Rules and the No-Undercut Property

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 175
Author(s):  
Gabriele Canna ◽  
Francesca Centrone ◽  
Emanuela Rosazza Gianin
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Coherent Risk Measures ◽  
Infinite Games ◽  
Allocation Rules ◽  
Coherent Risk ◽  
Allocation Problems ◽  
The One

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features that are related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures that are involved in capital allocation problems. We also discuss some problems and possible extensions that arise when we deal with non-coherent risk measures.

CAPITAL ALLOCATION FOR SET-VALUED RISK MEASURES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050009
Author(s):  
FRANCESCA CENTRONE ◽  
EMANUELA ROSAZZA GIANIN
Keyword(s):  
Convex Set ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Allocation ◽  
Allocation Rule ◽  
Scalar Case ◽  
Representation Theorems ◽  
Allocation Rules ◽  
The One ◽  
Definition Of

We introduce the definition of set-valued capital allocation rule, in the context of set-valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under some reasonable assumptions, we define some set-valued capital allocation rules relying on the representation theorems for coherent and convex set-valued risk measures and investigate their link with the notion of sub-differential for set-valued functions. We also introduce and study the set-valued analogous of some properties of classical capital allocation rules, such as the one of no undercut. Furthermore, we compare these rules with some of those mostly used for univariate (single-valued) risk measures. Examples and comparisons with the scalar case are provided at the end.

scholarly journals Surplus Sharing with Coherent Utility Functions

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Delia Coculescu ◽  
Freddy Delbaen
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Utility Functions ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Surplus Sharing ◽  
Insurance Business

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e., the shareholders.

scholarly journals Surplus Sharing with Coherent Utility Functions

2018 ◽  
Author(s):  
Delia Coculescu ◽  
Freddy Delbaen
Keyword(s):  
Risk Measures ◽  
Capital Allocation ◽  
Utility Functions ◽  
Coherent Risk Measures ◽  
Coherent Risk ◽  
Surplus Sharing ◽  
Insurance Business

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders.

scholarly journals Restricted Coherent Risk Measures and Actuarial Solvency

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Christos E. Kountzakis
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Insurance Company ◽  
Coherent Risk Measures ◽  
Dual Representation ◽  
Coherent Risk ◽  
Representation Form ◽  
Solvency Capital

We prove a general dual representation form for restricted coherent risk measures, and we apply it to a minimization problem of the required solvency capital for an insurance company.

scholarly journals Rearrangement Invariant, Coherent Risk Measures on L<sup>0</sup>

2015 ◽  
Vol 04 (01) ◽  
pp. 22-25
Author(s):  
Christos E. Kountzakis ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Risk Measures ◽  
Coherent Risk Measures ◽  
Coherent Risk
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