Set-valued average value at risk and its computation
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SubjectAverage value at risk; Set-valued risk measures; Coherent risk measures; Transaction costs; Benson’s algorithm
New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ’regulator’ version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both versions over finite probability spaces. Several examples illustrate various features of the theoretical constructions.
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Hamel, AH; Heyde, F (SIAM PUBLICATIONS, 2010)Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531-552] we define set-valued (convex) measures of risk and their acceptance sets, and we give dual representation theorems. A scalarization ...
Hamel, AH; Heyde, F; Rudloff, B (2011)Set-valued risk measures on Lpd with 0≤p≤∞ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are ...
Set Optimization and Applications - The State of the Art: From Set Relations to Set-Valued Risk Measures Hamel, AH; Heyde, F; Löhne, A; Rudloff, B; Schrage, C (Springer, 2015)This volume presents five surveys with extensive bibliographies and six original contributions on set optimization and its applications in mathematical finance and game theory. The topics range from more conventional ...