Capital allocation for cash-subadditive risk measures:From BSDEs toBSVIEs  

作　　者：Emanuela Rosazza Gianin Marco Zullino 

机构地区：[1]Department of Statistics and Quantitative Methods,University of Milano-Bicocca,20126 Milano,Italy [2]Department of Mathematics and Applications,University of Milano-Bicocca,20126 Milano,Italy

出　　处：《Probability, Uncertainty and Quantitative Risk》2024年第3期339-370,共32页概率、不确定性与定量风险（英文）

基　　金：financial support of Gnampa Research Project 2024 (Grant No.PRR-20231026-073916-203);funded in part by an Ermenegildo Zegna Founder's Scholarship (Zullino)。

摘　　要：In the context of risk measures,the capital allocation problem is widely studied in the literature where different approaches have been developed,also in connection with cooperative game theory and systemic risk.Although static capital allocation rules have been extensively studied in the recent years,only few works deal with dynamic capital allocations and its relation with BSDEs.Moreover,all those works only examine the case of an underneath risk measure satisfying cash-additivity and,moreover,a large part of them focuses on the specific case of the gradient allocation where Gateaux differentiability is assumed.The main goal of this paper is,instead,to study general dynamic capital allocations associated to cash-subadditive risk measures,generalizing the approaches already existing in the literature and motivated by the presence of(ambiguity on)interest rates.Starting from an axiomatic approach,we then focus on the case where the underlying risk measures are induced by BSDEs whose drivers depend also on the yvariable.In this setting,we surprisingly find that the corresponding capital allocation rules solve special kinds of Backward Stochastic Volterra Integral Equations(BSVIEs).

关 键 词：Risk measures Capital allocation BSDE BSVIE Cash-subadditivity SUBDIFFERENTIAL 

分 类 号：O175[理学—数学]