Consumption-Investment Problem with Transaction Costs for L\'evy-Driven Price Processes
Optimization and Control
2015-01-20 v1
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 L\'evy 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.
Keywords
Cite
@article{arxiv.1501.04361,
title = {Consumption-Investment Problem with Transaction Costs for L\'evy-Driven Price Processes},
author = {Dimitri De Vallière and Yuri Kabanov and Emmanuel Lépinette},
journal= {arXiv preprint arXiv:1501.04361},
year = {2015}
}