CCFEA Technical Report WP041-10 Symmetries and the Merton portfolio selection model
نویسنده
چکیده
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 an identical result to that obtained by Cox and Huang using measure theory and stochastic integrals. The nonlinear two-asset equation is then analyzed using Lie symmetry group theory. We show that the linearisation is directly related to the structure of the generalized symmetries.
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