Can stochastic discount factor appear in budget constraint of an agent

General DSGE Modeling
1

Dear Johannes,
Can stochastic discount factor appear in budget constraint of a household? the purpose is to discount future bond value using stochastic discount factor in household’s budget constaint?
Thank you very much!
Best regards,
Jesse

2

Without knowing more context, I would say no. The stochastic discount factor is something subjective (derived from the agents utility), while the budget constraint is about market prices. Of course, in equilibrium without e.g. borrowing constraints, there is a one-to-one relation between interest rates and the SDF, but that is an outcome, not part of the setup.

3

image
image1117×363 67.6 KB

image
image1138×410 63.4 KB

This paper is published in Journal of Economic Dynamics and Control, please see the attached PDF, the stochastic discount factor is used to discount future stochastic payoffs so as to represent bond price in the budget constraint, is this the explanation? thank youDSGE1.pdf|attachment (726.6 KB)

4

As I said, it is strictly speaking not correct to put the SDF at this stage. But if you do the correct setup where you put a price for the contingent claim in the budget constraint, you will get that this price is equal to the SDF in equilibrium. So the final result will be the same.