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

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	85-115
Number of pages	31
Journal	Finance and Stochastics
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s00780-010-0123-y
Publication status	Published - 1 Jan 2011

Keywords

Illiquid market
Integrodifferential equations
Optimal consumption
Optimal control
Semiconcavity
Sub/superdifferentials
Viscosity solutions

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10.1007/s00780-010-0123-y

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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",

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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

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DO - 10.1007/s00780-010-0123-y

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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

Abstract

Keywords

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