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Статья

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

Finance and Stochastics. 2016. Vol. 20. No. 3. P. 705-740.
De Vallière D., Kabanov Y., Lépinette E.

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.