Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

Details Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

2009-10-31

arxiv.org/abs/0911.0113v2

Economy

Quantitative Finance

Computational Finance

larger version with exact solutions, corrected typos, 13 pages, Symposium on Optimal Stopping in Abo/Turku 2009

Scientific paper

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.

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