Abstract: The study of risk measures began in a static environment with the
papers of Artzner et al. (1999) and Follmer and Schied (2002). To
incorporate information structure over time, static risk measures were
extended to a dynamic setting in Barrieu and El Karoui (2009), Jobert and
Rogers (2008), Yong (2007) and many others.
We are interested in a specific class of dynamic risk measures, namely
dynamic risk measures that arise as solutions of certain types of backward
stochastic differential equations (BSDEs) or backward stochastic Volterra
integral equations (BSVIEs). We will discuss this connection between risk
measures, capital allocations and BSDEs/BSVIEs and provide representation
results for dynamic risk measures and dynamic capital allocations. These
results are based on classical differentiability results for BSDEs/BSVIEs
and Girsanov-type change of measure arguments.
Joint work with Ludger Overbeck.