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Consumption-investment optimization problem in a Lévy financial model with transaction costs

De Vallière, Dimitri; Kabanov, Yuri; Lépinette, Emmanuel (2015), Consumption-investment optimization problem in a Lévy financial model with transaction costs, Finance and Stochastics, 20, 3, p. 705-740. 10.1007%2Fs00780-016-0303-5

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1501.04361
Date
2015-01
Journal name
Finance and Stochastics
Volume
20
Number
3
Publisher
Springer
Pages
705-740
Publication identifier
Metadata
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Author(s)
De Vallière, Dimitri
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Kabanov, Yuri
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider an optimal control problem for a linear stochastic integro-differential equation with conic constraints on the phase variable and with the control of singular–regular type. Our setting includes consumption-investment problems for models of financial markets in the presence of proportional transaction costs, where the prices of the assets are given by a geometric Lévy process, and the investor is allowed to take short positions. We prove that the Bellman function of the problem is a viscosity solution of an HJB equation. A uniqueness theorem for the solution of the latter is established. Special attention is paid to the dynamic programming principle.
Subjects / Keywords
Consumption-investment problem; Lévy process; Transaction costs; Bellman function; Dynamic programming; HJB equation; Lyapunov function
JEL
G13 - Contingent Pricing; Futures Pricing
G11 - Portfolio Choice; Investment Decisions