An incomplete equilibrium with a stochastic annuity

Kim Weston, Gordan Žitković

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimise 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 characterised by a system of fully coupled quadratic backward stochastic differential equations, a solution to which is proved to exist under Markovian assumptions. We also show that the equilibrium allocations lead to Pareto-optimal allocations only in exceptional situations.

Original languageEnglish (US)
Pages (from-to)359-382
Number of pages24
JournalFinance and Stochastics
Issue number2
StatePublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty


  • Annuity
  • BSDE
  • Incomplete markets
  • Radner equilibrium
  • Systems of BSDEs
  • Unspanned income


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