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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)

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JEROME DETEMPLE, Boston
To be announced

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

In the continuous-time 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 multi-stock incomplete diffusion market model with non-stationary 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 free-boundary 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  90098-1427, 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 risk-averse 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.