




Financial Mathematics / Mathématiques financières
(Cosponsored by MITACS and the Pacific Institute for the Mathematical
Sciences / Parrainée par MITACS et l'Institut Pacific pour les sciences
mathématiques) (Abel Cadenillas, Organizer)
 JEROME DETEMPLE, Boston
To be announced

 DANIEL DUFRESNE, University of Montreal, Montreal, Quebec H3C 3J7
Pricing Asian options

In the continuoustime framework, finding a formula for the price of
Asian opions is equivalent to finding the distribution of the integral
of geometric Brownian motion over a finite interval. I will talk about
this problem, and some of the recent advances towards its solution.
 ULRICH HAUSSMANN, Department of Mathematics, University of British Columbia,
Vancouver, British Columbia V6T 1Z2
Optimal portfolio selection based on observed prices

Consider a multistock incomplete diffusion market model with nonstationary
random coefficients. We solve the optimal portfolio selection problem in the
class of strategies which do not use direct observations of the appreciation
rates of the stocks, but rather use stock prices and an a priory given
distribution of the appreciation rates.
 MICHAEL TAKSAR, State University of New York, Stony Brook New York, USA
Optimal financing of a corporation subject to random returns

We consider the problem of finding an optimal financing mix of retained
earnings and external equity for maximizing the value of a corporation
in a stochastic environment. We formulate the problem as a singular
stochastic control for a diffusion process. We show that the value
function satisfies a freeboundary problem. We characterize the value
function and show that the optimal policy can be characterized in terms
of two threshold parameters. With asset level below the lower
threshold, optimal policy is to finance the firm's growth by retaining
all earnings and raising the required external equity financing. With
asset level above the higher threshold, optimal policy is to pay all
retained earnings as dividends and to bring in no new equity. Between
the two thresholds, the optimal policy is to retain all earnings but
not raise any external equity. We obtain an explicit solution for the
value function when there is no brokerage commission in floating
external equity. We provide economic interpretations of the results.
 FERNANDO ZAPATERO, Marshall School of Business, University of Southern
California, Los Angeles, Caifornia 900981427, USA
Executive stock options with effort disutility and choice of
volatility

We consider the problem of an executive that receives European call
options as compensation for her work. She can influence, with her
effort, the drift of the stock price. Besides, through the choice of
projects, she determines the level of volatility of the stock. The
executive is riskaverse and also experiences disutility from the level
of effort. We model such disutility as an increasing convex function.
Using convex duality techniques, we characterize the optimal level of
effort, as well as the optimal volatility. When the utility of the
executive is of the logarithmic type, we can express the controls in
closed form solution. Finally, we introduce the problem of the company
that wants to minimize overtime volatility and maximize final expected
value of the price of the stock. We characterize (and compute in
closed form for the previous case) the optimal strike price the company
will choose.

