Stability of Radner equilibria with respect to small frictions

Herdegen, Martin; Muhle‐Karbe, Johannes

doi:10.1007/s00780-018-0354-x

“…This yields the following expression for the liquidity premium: A similar result has been established for exponential investors in the limit for small transaction costs by [24]. In the present quadratic context, this result holds true exactly.…”

Section: Equilibrium Liquidity Premiasupporting

confidence: 78%

Equilibrium Liquidity Premia

Bouchard¹,

Fukasawa²,

Herdegen³

et al. 2017

SSRN Journal

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We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.Mathematics Subject Classification (2010): 91G10, 91G80.JEL Classification: C68, D52, G11, G12.

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“…Let us now interpret this result. A first observation is that if all agents are strategic and have the same risk aversion, then the frictionless equilibrium returns (3.1) also clear the market with transaction costs: A similar result has been established for exponential investors in the limit for small transaction costs by [24]. In the present quadratic context, this result holds true exactly.…”

Section: Equilibrium Liquidity Premiasupporting

confidence: 70%

Equilibrium returns with transaction costs

Bouchard

¹

,

Fukasawa

²

,

Herdegen

³

et al. 2018

Self Cite

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We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.Mathematics Subject Classification (2010): 91G10, 91G80.JEL Classification: C68, D52, G11, G12. We are grateful to Michalis Anthropelos, Peter Bank, Paolo Guasoni, and Felix Kübler for stimulating discussions and detailed comments. Moreover, we thank an anonymous referee for his or her careful reading and pertinent remarks.

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“…This is needed to study the small-cost asymptotics of expected utility maximization problems rather than the pathwise, quadratic criteria of [9]. Unlike for singularly-or impulse-controlled deviations (where integrability is inherited directly from the corresponding trading boundaries [1,14,19]), this necessitates further delicate estimates that require the following integrability assumptions on the processes b, c, L, M, H, K appearing in the SDE for X ε and the scaling limit (1.4): 4…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Scaling limits of processes with fast nonlinear mean reversion

Cayé

¹

,

Herdegen

²

,

Muhle‐Karbe

³

2020

Stochastic Processes and their Applications

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We derive scaling limits for integral functionals of Itô processes with fast nonlinear meanreversion speeds. In these limits, the fast mean-reverting process is "averaged out" by integrating against its invariant measure. The convergence is uniformly in probability and, under mild integrability conditions, also in S p . These results are a crucial building block for the analysis of portfolio choice models with small superlinear transaction costs, carried out in the companion paper of the present study [11].Mathematics Subject Classification (2010): 60F25, 60H10.Keywords: processes with fast nonlinear mean reversion; scaling limits * We are grateful to two anonymous referees for extremely detailed and helpful comments that have greatly improved the final version of this manuscript.

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Stability of Radner equilibria with respect to small frictions

Cited by 20 publications

References 71 publications

Equilibrium Liquidity Premia

Equilibrium Liquidity Premia

Equilibrium returns with transaction costs

Scaling limits of processes with fast nonlinear mean reversion

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