


Financial Mathematics / Mathématiques financières (Org: Luis Seco)
 ROBERT ALMGREN, University of Toronto, Toronto, Ontario
Continuoustime model for household portfolios
[PDF] 
We develop a continuoustime model for a Mertonlike household
portfolio choice problem in which the investor is subject to
undiversifiable income risk. A meanreverting factor predicts excess
return of the stock, and wealth must be allocated among investments and
consumption. The investor's goal is to maximize the utility of
lifetime consumption in the presence of shortsales and borrowing
constraints. Using techniques of stochastic optimal control, we derive
a nonlinear PDE with an internal free boundary. For a reduced
problem, we obtain numerical solution for the value function and thus
for the optimal portfolio policies. [Joint work with Raymond Cheng]
 IAN BUCKLEY, Centre for Quantitative Finance, Imperial College, London, UK
Portfolio optimization for alternative investments
[PDF] 
(With Gustavo Comezana, Ben Djerroud and Luis Seco.)
A tractable and practical generalization to Markowitz meanvariance
style portfolio theory is presented in which portfolios of hedge funds
and commodity trading advisors (CTAs) can be handled successfully.
Making the assumption that their returns have the finite Gaussian
mixture distribution and using the probability of outperforming a
target return as the objective function, these assets are optimized in
the static setting by solving a nonlinear programming problem to find
portfolio weights.
 ABEL CADENILLAS, Department of Mathematical and Statistical Sciences,
University of Alberta, Edmonton, Alberta T6G 2G1
Optimal stochastic impulse control of the free cash flow
[PDF] 
We apply the theory of stochastic impulse control to the determination
of the optimal policy for cash disbursements and seasonal equity
offerings of a financial corporation.
 TAHIR CHOULLI, Alberta
Minimal Hellinger martingale measures in incomplete markets
[PDF] 
In incomplete markets, one of the crucial problem that we face is
concerned with the choice of an ``appropiate'' riskneutral measure to
price any payoff. Via Hellinger processes, optimal criterions are
proposed. These criterions are charaterized by the explicite forms for
the extremal martingale measures as well as the control of markets'
information dynamically. Hence the methodology illustrates an interplay
between control and information theories. The relationship of the
obtained martingale measures and the existing ones is investigated. The
existence and comparison results are detailed in the general
semimartingale framework.
 ALI LAVASSANI, Calgary
[PDF] 
 ERIC RENAULT, Université de Montréal, CIREQ, CIRANO
Stochastic volatility models
[PDF] 
(Joint work with F. Comte and L. Coutin).
In this paper, we study a classical extension of the Black and Scholes
model for asset prices and option pricing, generally known as the
Heston model. In our specification, the volatility is a fractional
integral of a Cox, Ingersoll, Ross process (also known as an ``affine''
model): this implies that it is not only stochastic but also admits
long memory features. We study the volatility and the integrated
volatility processes and prove their long memory properties. We address
the issue of option pricing and we study discretizations of the model.
Lastly, we provide an estimation strategy and simulation experiments in
order to test this methodology.
 TOM SALISBURY, Department of Mathematics and Statistics, York University,
Toronto, Ontario M3J 1P3
Liquidity premiums for variable annuities
[PDF] 
A significant level of US retirement savings are housed in variable
annuity accounts. Such accounts typically impose restrictions on how
funds can be moved around. What premium should these accounts pay in
order to compensate the investor for the resulting lack of liquidity?
The problem can be solved by reformulating it in such a way that
techniques from the theory of American Options can be applied. This is
joint work with Moshe Milevsky, Sid Browne, and Shannon Kennedy.
 DAVE SAUNDERS, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
Optimal structuring of asset portfolios for insurance products
with minimum guarantee provisions
[PDF] 
Modern insurance products are becoming increasingly complex, offering
various guarantees, surrender options and bonus provisions. Typical
products allow investors to participate in the returns of a reference
portfolio, subject to some minimum guaranteed floor on the level of
returns. The optionlike nature of the payout to the investor is
evident, and much work has been done on finding appropriate pricing
algorithms under various assumptions on the stochastic behaviour of the
reference portfolio and market risk factors. Little effort has been
devoted to the problem of optimally structuring the reference
portfolio. We consider this problem from the point of view of the firm
offering the product. The resulting optimization problem is a nonlinear
stochastic programming problem. We discuss properties of its solution
and different solution algorithms. Examples illustrate how the model
can be used to analyze different policy features and offer the
optimally structured product for investors and shareholders.
 GEORGE STOICA, University of New Brunswick, Saint John, New Brunswick
Market completeness: a return to order
[PDF] 
We define a trading strategy operator in a twotimes stochastic economy
and investigate market completeness with respect to the order relation
on a linear lattice of functions describing, in a twotimes economy,
the associated cash flow space. The study is leading us towards
alternative definitions for market completeness, in terms of trading
strategy operators and approximate uniformly integrable martingales
spanning on such linear lattices. In particular, we study the almost
everywhere convergence situation on the space of cash flows given by
the space of all equivalence classes of real valued random variables.
 AGNES TOURIN, Department of Mathematics and Statistics, McMaster University,
Hamilton, Ontario L8S 4L8
Maximizing the probability of being solvent in the presence
of transaction costs
[PDF] 
It is a well known result that, in the presence of transaction costs,
the writer of a European option may not be solvent. Here, we present a
stochastic control problem which consists in maximizing the probability
of being solvent. We compute the optimal probability and the free
boundaries characterizing the optimal policies. This is a joint work
with Thaleia Zariphopoulou.
 TONY WARE, University of Calgary, Calgary, Alberta
Numerical explorations of swing options
[PDF] 
We describe some partial differential equation models for swing option
pricing, and discuss the issue of calibrating those models to the
relevant markets. We also describe a finite element scheme for solving
the equations and illustrate the characteristics of these options by
means of a set of numerical explorations.

