publication . Article . Preprint . 2016

Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Kramkov, Dmitry; Pulido, Sergio;
Open Access English
  • Published: 16 Aug 2016
  • Publisher: HAL CCSD
Abstract
We obtain stability estimates and derive analytic expansions for local solutions of multi-dimensional quadratic BSDEs. We apply these results to a financial model where the prices of risky assets are quoted by a representative dealer in such a way that it is optimal to meet an exogenous demand. We show that the prices are stable under the demand process and derive their analytic expansions for small risk aversion coefficients of the dealer.
Subjects
free text keywords: multi-dimensional quadratic BSDEs,stability of quadratic BSDEs,asymptotic behavior of quadratic BSDEs,liquidity,price impact, multi-dimensional quadratic BSDEs, stability of quadratic BSDEs, asymptotic behavior of quadratic BSDEs, liquidity, price impact, JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D53 - Financial Markets, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G12 - Asset Pricing • Trading Volume • Bond Interest Rates, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C62 - Existence and Stability Conditions of Equilibrium, [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [QFIN.PM]Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], [QFIN.TR]Quantitative Finance [q-fin]/Trading and Market Microstructure [q-fin.TR], JEL : D.D5.D53, JEL : G.G1.G12, JEL : C.C6.C62, [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN.PM] Quantitative Finance [q-fin]/Portfolio Management [q-fin.PM], [QFIN.TR] Quantitative Finance [q-fin]/Trading and Market Microstructure [q-fin.TR], Quantitative Finance - Mathematical Finance, Mathematics - Probability, Quantitative Finance - Portfolio Management, Quantitative Finance - Trading and Market Microstructure, 60H10, 91B24, 91G80, Finance, Applied Mathematics, Numerical Analysis, Financial modeling, Market liquidity, Economics, Econometrics, Quadratic equation, Risk aversion, Impact model, Mathematical optimization
Funded by
EC| POLYTE
Project
POLYTE
Polynomial term structure models
  • Funder: European Commission (EC)
  • Project Code: 307465
  • Funding stream: FP7 | SP2 | ERC
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publication . Article . Preprint . 2016

Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model

Kramkov, Dmitry; Pulido, Sergio;