An incomplete equilibrium with a stochastic annuity
Mathematical Finance
2018-09-18 v1
Abstract
We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market consists of a traded annuity, and, along with unspanned income, the market is incomplete. Set in a Brownian framework, the income is driven by a multidimensional diffusion, and, in particular, includes mean-reverting dynamics. The equilibrium is characterized by a system of fully coupled quadratic backward stochastic differential equations, a solution to which is proved to exist under Markovian assumptions.
Keywords
Cite
@article{arxiv.1809.05947,
title = {An incomplete equilibrium with a stochastic annuity},
author = {Kim Weston and Gordan Zitkovic},
journal= {arXiv preprint arXiv:1809.05947},
year = {2018}
}