Consumption-investment problem with transaction costs for Lévy-driven price processes

Dimitri Vallière, Yuri Kabanov () and Emmanuel Lépinette
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Dimitri Vallière: Université de Franche-Comté
Yuri Kabanov: Université de Franche-Comté
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Finance and Stochastics, 2016, vol. 20, issue 3, No 5, 705-740

Abstract: Abstract 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.

Keywords: Consumption-investment problem; Lévy process; Transaction costs; Bellman function; Dynamic programming; HJB equation; Lyapunov function; 60G44 (search for similar items in EconPapers)
JEL-codes: G11 G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00780-016-0303-5

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