Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
