Optimal consumption policies in illiquid markets

Alessandra Cretarola; Fausto Gozzi; Huyên Pham; Peter Tankov

doi:10.1007/s00780-010-0123-y

Optimal consumption policies in illiquid markets

Alessandra Cretarola
, Fausto Gozzi
, Huyên Pham
, Peter Tankov

Dipartimento di Scienze Economiche
LUISS University
Laboratoire de Probabilités et Modelèles Aléatoires
Institut Universitaire de France

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

13 Citations (Scopus)

Résumé

We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613-627, 2008). Our main result is to derive smoothness C¹ results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.

langue originale	Anglais
Pages (de - à)	85-115
Nombre de pages	31
journal	Finance and Stochastics
Volume	15
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00780-010-0123-y
état	Publié - 1 janv. 2011

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title = "Optimal consumption policies in illiquid markets",

abstract = "We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613-627, 2008). Our main result is to derive smoothness C1 results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.",

keywords = "Illiquid market, Integrodifferential equations, Optimal consumption, Optimal control, Semiconcavity, Sub/superdifferentials, Viscosity solutions",

author = "Alessandra Cretarola and Fausto Gozzi and Huy{\^e}n Pham and Peter Tankov",

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T1 - Optimal consumption policies in illiquid markets

AU - Cretarola, Alessandra

AU - Gozzi, Fausto

AU - Pham, Huyên

AU - Tankov, Peter

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613-627, 2008). Our main result is to derive smoothness C1 results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.

AB - We investigate optimal consumption policies in the liquidity risk model introduced by Pham and Tankov (Math. Finance 18:613-627, 2008). Our main result is to derive smoothness C1 results for the value functions of the portfolio/consumption choice problem. As an important consequence, we can prove the existence of the optimal control (portfolio/consumption strategy) which we characterize both in feedback form in terms of the derivatives of the value functions and as the solution of a second-order ODE. Finally, numerical illustrations of the behavior of optimal consumption strategies between two trading dates are given.

KW - Illiquid market

KW - Integrodifferential equations

KW - Optimal consumption

KW - Optimal control

KW - Semiconcavity

KW - Sub/superdifferentials

KW - Viscosity solutions

U2 - 10.1007/s00780-010-0123-y

DO - 10.1007/s00780-010-0123-y

M3 - Article

AN - SCOPUS:78651447545

SN - 0949-2984

VL - 15

SP - 85

EP - 115

JO - Finance and Stochastics

JF - Finance and Stochastics

IS - 1

ER -

Optimal consumption policies in illiquid markets

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