Symmetry-based solution of a model for a combination of a risky investment and a riskless investment

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:334

Article

Leach, P. G. L. ; O'Hara, J. G. ; Sinkala, W.

关键词: mean-reversion;    portfolio selection;    Lie symmetry;   

DOI  :  10.1016/j.jmaa.2006.11.056

来源: Elsevier

【 摘 要 】

Benth and Karlsen [F.E. Benth, K.H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stoch. Anal. Appl. 23 (200:5) 687-704] treated a problem of the optimisation of the selection of a portfolio based upon the Schwartz mean-reversion model. The resulting Hamilton-Jacobi-Bellman equation in 1 + 2 dimensions is quite nonlinear. The solution obtained by Benth and Karlsen was very ingenious. We provide a solution of the problem based on the application of the Lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions. (c) 2007 Elsevier Inc. All rights reserved.

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