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Symmetry-based solution of a model for a combination of a risky investment and a riskless investment |
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| Authors: | PGL Leach JG O'Hara |
| Institution: | a School of Mathematical Sciences, Howard College, University of KwaZulu-Natal, Durban 4041, South Africa b School of Statistics and Actuarial Science, Howard College, University of KwaZulu-Natal, Durban 4041, South Africa c Department of Mathematics and Applied Mathematics, Faculty of Science and Engineering, Walter Sisulu University, Private Bag X1, Mthatha 5117, South Africa |
| Abstract: | 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 (2005) 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. |
| Keywords: | Mean-reversion Portfolio selection Lie symmetry |
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