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Mathematics of Finance / Mathématiques financières
(Hassan Manouzi, Organizer)

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TAHIR CHOULLI, Alberta
An optimization model for a company with constraints on risk control

In this talk I will discuss a model of a corporation which faces constant liability payments and which can choose a production/business policy from an available set of control policies with different expected profits and risks. The main feature here is that there are constraints on business activities such as inability to completely eliminate risk or when such a risk cannot exceed a certain level. The objective is to find a business policy and a dividend distribution scheme so as to maximize the expected present value of the total dividend distributions. This leads to a mixed regular-singular stochastic control problem. A complete and explicit analysis of the Hamilton-Jacobi-Bellman equation resulting from this control problem is provided. The optimal policies with their economic interpretations are detailed as well.

ABDESSAMAD KAREM, de Caen, France
Volatlité du CAC40 et changements structurels

(Travail realise en collaboration avec Ahmed Louichi)

La dynamique du CAC40 est explorée sur une longue période. La volatilit é de la série est moélisée par des processus ARCH, GARCH, GARCH-L et t-GARCH. le problème de la persistence est appréhendé à travers les changements structurels de la série par une spécification SWARCH due à J. Hamilton et R. Sumsel.

ROGEMAR MAMON, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario  N2L 3G1
A synthesis of interest rate derivative pricing under the forward measure

We consider two versions of the contingent claim valuation formula: one expressed in terms of the martingale measure and the other in terms of the forward measure. Based on previous work with Elliott, the equivalence of these two representations is shown. For almost all types of derivative instruments in the interest rate market, the forward measure approach is illustrated to be the natural and convenient choice. Within a certain class of exponential affine models, the short rate dynamics under the forward measure are obtained through the change of measure technique of Geman et al. (1995). In particular, closed-form pricing solutions are obtained for interest rate derivatives whose payoff functions fall into one of these categories: linear in the state variable, exponential affine or in integro-linear forms. Furthermore, for each term structure model being considered a specification of several alternative bond pricing derivations, including the explicit use of the forward measure will also be given.

GEORGE STOICA, University of New Brunswick-Saint John Campus, Department of Mathematical Sciences, Saint John, New Brunswick  E2L 4L5
Spike prices and spectrum swings

Based on multidimensional discontinuous processes with eventually discontinuous coefficients, many models for electricity have been employed. Under appropriate calibration, those models explain the skewness and excess kurtosis observed in the model's distribution, but the only one whose spikes are ``not scarce and thin enough'' is Martin Barlow's.

Because the spikes are the main feature in electricity modelling, in this talk we forget about skewness and kurtosis, and relate the practical success of Barlow's model to the associated generator's behavior in the area where its spectrum, from discrete, turns to continuous. Secondly, for a wide range of parameters including the spikes-producing ones, we obtain a series expansion for the price function of a European contingent claim written on Barlow's model; its coefficients can be computed easily using standard approximating methods.

RUPPA K. THULASIRAM, Department of Computer Sciencem University of Manitoba, Winnipeg, Manitoba  R3T 2N2
A second order L₀ stable algorithm for evaluating European options

In this paper, we study the option pricing problem, one of the prominent and challenging problems in computational finance. Using Pade approximation, we have developed a second order L₀ stable discrete parallel algorithm for experimentation on advanced architectures. This algorithm is suitable for more complicated option pricing problems. For simulation purposes, we have implemented the sequential version of this algorithm and evaluated the European Options. Numerical results are compared with those obtained using other commonly used numerical methods and shown that the new algorithm is robust and efficient than the traditional schemes.