Temporal aggregation of the Aumann-Serrano and Foster-Hart performance indexes

Year：2020 NO：20001 Author：Jiro Hodoshima

We consider temporal aggregation of the Aumann-Serrano (AS) and Foster-Hart (FS) performance indexes proposed by Kadan and Liu (2014). The AS performance index is closed under temporal aggregation when the underlying discrete observations are independently and identically distributed and the underlying continuous stochastic process is a Lévy process. The FH performance index is closed under temporal aggregation when the underlying discrete observations are identically distributed and the underlying continuous stochastic process is a stationary process if an approximation of the implicit equation by the Taylor series expansion up to the first order is valid. We present empirical examples using U.S. stock return data.

---