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

2015/01/18 by De Vallière, Dimitri, Kabanov, Yuri, Lépinette, Emmanuel
#FOS: Mathematics #G11 #G13 #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1501.04361

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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