A note on the integrability of the classical portfolio selection model

作者：Naicker V; O'Hara J G^*; Leach P G L

来源：Applied Mathematics Letters, 2010, 23(9): 1114-1119.

DOI：10.1016/j.aml.2010.04.046

• Lie symmetry analysis
• Portfolio selection theory
• Differential equations

We revisit the classical Merton portfolio selection model from the perspective of integrability analysis. By an application of a nonlocal transformation the nonlinear partial differential equation for the two-asset model is mapped into a linear option valuation equation with a consumption dependent source term. This result is identical to the one obtained by Cox-Huang [J.C. Cox, C-f. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory 49 (1989) 33-88], using measure theory and stochastic integrals. The nonlinear two-asset equation is then analyzed using the theory of Lie symmetry groups. We show that the linearization is directly related to the structure of the generalized symmetries.

• 出版日期2010-9