Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions
AbstractWe study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal systems of subalgebras and the complete set of non-equivalent reductions of studied PDEs to ODEs. In most cases we obtain families of exact solutions or derive particular solutions to the equations.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1002.0864.
Date of creation: Feb 2010
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Publication status: Published in Lobachevskii Journal of Mathematics , 2010,vol. 31,no 2, pp.90-99; ISSN 1995-0802
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-02-20 (All new papers)
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