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.
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The research is funded by the grant \(n^{\circ}\)14.A12.31.0007 of the Government of the Russian Federation.
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De Vallière, D., Kabanov, Y. & Lépinette, E. Consumption-investment problem with transaction costs for Lévy-driven price processes. Finance Stoch 20, 705–740 (2016). https://doi.org/10.1007/s00780-016-0303-5
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DOI: https://doi.org/10.1007/s00780-016-0303-5
Keywords
- Consumption-investment problem
- Lévy process
- Transaction costs
- Bellman function
- Dynamic programming
- HJB equation
- Lyapunov function