A stochastic linear-quadratic problem with Lévy processes and its application to finance

Ken-ichi Mitsui and Yoshio Tabata

Stochastic Processes and their Applications, 2008, vol. 118, issue 1, 120-152

Abstract: We study a Linear-Quadratic Regulation (LQR) problem with Lévy processes and establish the closeness property of the solution of the multi-dimensional Backward Stochastic Riccati Differential Equation (BSRDE) with Lévy processes. In particular, we consider multi-dimensional and one-dimensional BSRDEs with Teugel's martingales which are more general processes driven by Lévy processes. We show the existence and uniqueness of solutions to the one-dimensional regular and singular BSRDEs with Lévy processes by means of the closeness property of the BSRDE and obtain the optimal control for the non-homogeneous case. An application of the backward stochastic differential equation approach to a financial (portfolio selection) problem with full and partial observation cases is provided.

Keywords: Linear-quadratic; regulators; Lévy; process; Backward; stochastic; (Riccati); differential; equation; Regular; and; singular; case (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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