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arXiv · 1501.04361

Consumption-Investment Problem with Transaction Costs for Lévy-Driven Price Processes

Dimitri De Vallière·Yuri Kabanov·Emmanuel Lépinette
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Abstract

We consider an optimal control problem for a linear stochastic integro-diffe\-rential equation with conic constraints on the phase variable and 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 price 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 the HJB equation. A uniqueness theorem for the solution of the latter is established. Special attention is paid to the Dynamic Programming Principle.

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Dimitri De Vallière, Yuri Kabanov, Emmanuel Lépinette. 2015-01-18. Consumption-Investment Problem with Transaction Costs for Lévy-Driven Price Processes. https://arxiv.org/abs/1501.04361

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