On the Relation between Linearity-Generating Processes and Linear-Rational Models

Damir Filipović*, Martin Larsson, Anders Bjerre Trolle

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We review the notion of a linearity-generating (LG) process introduced by Gabaix and relate LG processes to linear-rational (LR) models studied by Filipović et al. We show that every LR model can be represented as an LG process and vice versa. We find that LR models have two basic properties that make them an important representation of LG processes. First, LR models can be easily specified and made consistent with nonnegative interest rates. Second, LR models go naturally with the long-term risk factorization due to Alvarez and Jermann, Hansen and Scheinkman, and Qin and Linetsky. Every LG process under the long forward measure can be represented as a lower dimensional LR model.
Original languageEnglish
JournalMathematical Finance
Issue number3
Pages (from-to)804-826
Number of pages23
Publication statusPublished - Jul 2019
Externally publishedYes

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