Past Seminars

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The Volume Weighted Average Price Option
Antony Stace
University of Queensland
Start time: 11:00 am
Date: Thursday 16 March 2006
Location: Room 216, Prentice Building (42), University of Queensland

In this talk I introduce the volume weighted average price (VWAP) option. VWAP options have a payoff that is dependent on both the stock price and volume of stock traded over the lifetime of the option. I give some real work examples of both the VWAP price and VWAP options. Following this, I describe several different methods that I have developed to price VWAP options. I concentrate on the valuation of European style, fixed and floating strike call options. Little additional effort is required to adapt the results of this work to value puts.

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Bounds for the decay parameter of a general birth-death process
David Sirl
University of Queensland
Start time: 11:00 am
Date: Thursday 9 March 2006
Location: Room 216, Prentice Building (42), University of Queensland

In the study of continuous-time Markov chains with state spaces consisting of an absorbing state, which is accessible from an irreducible transient class, the so-called decay parameter is of fundamental importance. Aside from being of interest in its own right, the decay parameter plays a central role in the theory of the quasi-stationary distributions of such processes. Despite its importance, it is notoriously difficult to evaluate or even approximate. We outline its significance in the aforementioned contexts, then introduce an alternative characterisation and indicate how this leads to explicit bounds for the value of the decay parameter of a general birth-death process in terms of the birth and death rates only. An immediate corollary is a necessary and sufficient condition for positivity of the decay parameter. We illustrate the power of these results with several examples. This is joint work with Hanjun Zhang and Phil Pollett

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An exactly solvable model of recombination, mutation and selection
Professor Michael Baake
University of Bielefeld, Germany
Start time: 11:00 am
Date: Wednesday 1 March 2006
Location: Richard Berry Building, The University of Melbourne

Population genetics is concerned with the time evolution of a large ensemble of individuals, represented by their genetic sequences. The latter, in the course of reproduction, change under the influence of mutation, selection, recombination and various other factors. Though this is a problem of stochastic nature, important and relevant information can be extracted from its deterministic infinite population limit, which leads to a system of nonlinear differential equations. In this talk, starting from the case of pure recombination, a relevant continuous time case is discussed that can be solved exactly. In a second step, this exact solution is extended to include arbitary mutation and additive selection. This could serve as the starting point for further extensions of perturbative type and should be more realistic than the models of neutral evolution used so far.

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Maritime Path Planning in Minefield Threat Environments
Ranga Muhandiramge
University of Western Australia
Start time: 2:15 pm
Date: Thursday 2 February 2006
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton.

The Defense Science and Technology Organization (DSTO) have funded a project to investigate the ways in which mathematics, and in particular operations research, may be helpful in the problem of minefield path transit at sea. These include finding minimum risk paths and detection/clearance of mines. Many different models of the problem will be formulated and solved using different network algorithms. Of particular interested is network weight constrained shortest path problem (WCSPP) formulation and its relation to the continuous version of the problem. Improvements to the WCSPP algorithm will also be presented.

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Some Properties of Principal Components Analysis for Functional Data
Mr Mohammad Hosseini-Nasab
Australian National University
Start time: 2:15 pm
Date: Thursday 1 December 2005
Location: Theatre 2, Old Geology Building, The University of Melbourne

Functional data analysis is intrinsically infinite-dimensional; functional principal component analysis, or PCA, reduces dimension to a finite level, and points to the most significant components of the data. However, while this technique is often discussed, its properties are not as well understood as they might be. In this talk, it is shown how the properties of functional PCA can be elucidated through stochastic expansions and related results. The approach quantifies the errors that arise through statistical approximation, in successive terms of orders $n^{-1/2}, n^{-1}, n^{-3/2}$,..., where $n$ denotes sample size. The expansions show how spacings among eigenvalues impact on statistical performance. The results can be used to explore properties of existing methods, and also to suggest new techniques. In particular, we suggest bootstrap methods for constructing simultaneous confidence regions for an infinite number of eigenvalues, and also for individual eigenvalues and eigenvectors.

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