An incomplete equilibrium with a stochastic annuity

Kim Weston () and Gordan Žitković ()
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Kim Weston: Rutgers University
Gordan Žitković: The University of Texas at Austin

Finance and Stochastics, 2020, vol. 24, issue 2, No 4, 359-382

Abstract: Abstract 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.

Keywords: Incomplete markets; Radner equilibrium; Annuity; BSDE; Systems of BSDEs; Unspanned income; 91B51; 60H30; 91B25 (search for similar items in EconPapers)
JEL-codes: D52 G12 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s00780-020-00415-6

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