Down-side risk minimization under prescribed consumption level

Issue title: Stochastic Control

Article type: Research Article

Authors: Nagai, Hideo

Affiliations: Division of Mathematical Science for Social Systems, Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan. E-mail: [email protected]

Abstract: We are interested in exploring methodology to estimate small probabilities of rare events from the view points of stochastic control. In particular, we study portfolio choice to be selected by an investor possessing several kinds of securities under prescribed consumption level, who is considering minimizing down-side risk probability for his (her) total wealth of falling below a given target growth rate in the long term. We shall show the problem finding the strategy minimizing such probability is considered large deviations control. From this viewpoint we shall state about general asymptotic theory for factor models, explicit calculation for linear Gaussian models, and consideration in the case of complete market models.

Keywords: Large deviation, long-term investment and consumption, risk-sensitive stochastic control, H–J–B equation of ergodic type

DOI: 10.3233/RDA-2011-0058

Journal: Risk and Decision Analysis, vol. 3, no. 3, pp. 191-200, 2012