### Abstract

Original language | English |
---|---|

Article number | 12 |

Number of pages | 32 |

Journal | Nonlinear Differential Equations and Applications |

Volume | 24 |

Issue number | 2 |

Early online date | 18 Feb 2017 |

DOIs | |

State | Published - Apr 2017 |

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### Cite this

*Nonlinear Differential Equations and Applications*,

*24*(2), [12]. DOI: 10.1007/s00030-017-0435-0

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*Nonlinear Differential Equations and Applications*, vol 24, no. 2, 12. DOI: 10.1007/s00030-017-0435-0

**Option prices under liquidity risk as weak solutions of semilinear diffusion equations.** / Fahrenwaldt, Matthias Albrecht; Roch, Alexandre F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Option prices under liquidity risk as weak solutions of semilinear diffusion equations

AU - Fahrenwaldt,Matthias Albrecht

AU - Roch,Alexandre F.

PY - 2017/4

Y1 - 2017/4

N2 - Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to option prices as defined in terms of replication in a probabilistic setup. We obtain an asymptotic representation of the price and the hedging strategy as a liquidity parameter converges to zero.

AB - Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to option prices as defined in terms of replication in a probabilistic setup. We obtain an asymptotic representation of the price and the hedging strategy as a liquidity parameter converges to zero.

U2 - 10.1007/s00030-017-0435-0

DO - 10.1007/s00030-017-0435-0

M3 - Article

VL - 24

JO - Nonlinear Differential Equations and Applications

T2 - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

SN - 1021-9722

IS - 2

M1 - 12

ER -