Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions

Details Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions

2010-08-16

arxiv.org/abs/1008.2663v1

Economy

Quantitative Finance

Pricing of Securities

17 pages, 3 figures

Scientific paper

We study the general model of self-financing trading strategies in illiquid markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(alpha). This function is deep connected to an utility function. We describe the Lie symmetry algebra of this PDE and provide a complete set of reductions of the PDE to ordinary differential equations (ODEs). In addition we are able to describe all types of functions g(alpha) for which the PDE admits an extended Lie group. Two of three special type functions lead to models introduced before by different authors, one is new. We clarify the connection between these three special models and the general model for trading strategies in illiquid markets. We study with the Lie group analysis the new special case of the PDE describing the self-financing strategies. In both, the general model and the new special model, we provide the optimal systems of subalgebras and study the complete set of reductions of the PDEs to different ODEs. In all cases we are able to provide explicit solutions to the new special model. In one of the cases the solutions describe power derivative products.

Affiliated with

Also associated with

No associations

Rating

Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-177696