




Mathematics of Finance / Mathématiques financières (Hassan Manouzi, Organizer)
 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 regularsingular
stochastic control problem. A complete and explicit analysis of the
HamiltonJacobiBellman 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, GARCHL et tGARCH. 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, closedform 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
integrolinear 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 BrunswickSaint 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
spikesproducing 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 L_{0} 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 L_{0}
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.

