## Abstract

In a fairly recent paper (2008 American Control Conference, June 11-13, 1035-1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal-value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution.

Original language | English |
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Pages (from-to) | 4448-4460 |

Number of pages | 13 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 38 |

Issue number | 17 |

DOIs | |

Publication status | Published - 30 Nov 2015 |

## Keywords

- evolution partial differential equations
- financial mathematics
- Lie symmetries
- stochastic control