For more information about this meeting, contact Anna Mazzucato, Manfred Denker, Victor Nistor.

Title: | The generalized binomial model under stationary increments |

Seminar: | Probability and Financial Mathematics Seminar |

Speaker: | Manfred Denker, PSU |

Abstract: |

The binomial model for a stock price uses independent two-state processes for the increments of the modelling process. I will show that independence is not crucial. A new uniform local limit theorem for stationary processes will be discussed: Let $T$ be a piecewise expanding map on the interval and $f$ be a $\mathbb Z^d$-valued $L_2$-function. The local limit theorem states that $n^{(d-1)/2}Leb(\{x: f(x)+...+f(T^n(x)) = (n_1,...,n_d)\})$ is approximately the value of a $d$-dimensional normal distribution whenever $(n_1,...,n_d)$, the approximation being valid for $(n_1,...,n_d)$ uniformly in large regions. This approach gives new Black-Scholes type formulas for option prices. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 03 / 15 / 2011 |

Time: | 04:00pm - 05:00pm |