Grant: Discovery Grants Program - Individual

The objective of this research program is to develop mathematical models and efficient algorithms to solve practical decision-making problems that are dynamic in nature and involve a level of uncertainty. Three specific areas of application will be considered: financial derivatives, long-term environmental-protection agreements, and firms' strategic investment decisions. The evaluation of financial derivatives often requires numerical procedures. A first objective is to increase the efficiency of existing algorithms, so that they can be used to price derivatives that depend on multiple factors. A second objective is to adapt these solution approaches to more realistic market models, and more specifically, to account for time-varying volatility and for the transaction costs of hedging strategies. A growing concern is how to secure the continuing participation of countries in International Environmental Agreements over time. A first objective is to study how the stability of such agreements is affected by uncertainty about key parameters such as climate-change sensitivity or the economic impacts of pollution. A second objective is to study an alternative equilibrium concept, in which countries are assumed to foresee the impacts that their defection would have on other participants in the agreement. The making and timing of major investment decisions by firms, including investment in R&D, technology upgrades, or new ventures, can also be set up as dynamic optimization problems under uncertainty. We will model and solve for various strategic decisions by the firm. A first example involves a decision about a biogas-investment project. A second example is the adoption of new technology by a firm, assuming that, each time technology is updated, the firm incurs a learning cost that decreases over time.