Grant: Discovery Grants Program - Individual

The objective of this research program is to develop mathematical models and efficient computational algorithms to solve practical strategic decision-making problems in a dynamic and uncertain context. Two specific application areas will be considered: investment finance and natural resource management. Although these application areas are very different from each other, they share a common methodological approach, that is, stochastic dynamic optimization in a multidimensional framework. In both these areas, solving realistic problems requires the development of efficient numerical methods. Thus, in addition to addressing these specific issues, a broader objective of this research program is to develop innovative methods for numerically solving large-scale stochastic dynamic problems and multi-stage dynamic games, thereby contributing to the advancement of knowledge in the field of decision-making under uncertainty. In the aftermath of the 2008 financial crisis, two important issues in investment finance are managing risk and ensuring compliance with the corresponding regulatory requirements (e.g. capital charge adjustments to account for counterparty risk). While investment finance has all the essential ingredients of dynamic games, where investors, firms, and financial intermediaries have competing interests and interact strategically over time, most valuation models are built from a single perspective. The objectives of our first line of research are to incorporate a strategic dimension in valuation and hedging models, and to develop new computational methods that can be used for realistic scenarios involving multidimensional investment portfolios. In practice, procedures used for risk management and regulatory compliance must be used in real time and should provide accurate results within seconds. A growing concern in environmental and resource management is related to the so-called tragedy of the commons. Access to a common resource (air quality, biodiversity, high-seas fishing) leads to overexploitation and, potentially, to catastrophic consequences. One of the means employed to prevent this from happening is the establishment of agreements between stakeholders (e.g. multilateral agreements under the aegis of the United Nations), to ensure that resources are managed in the best interest of all, including future generations. The objective of our second line of research is to study how the design, stability and implementability of environmental agreements are affected by dynamics and uncertainty, and by the participants' foresight and strategic outlooks. In this context, foresight is defined as the players' ability to account for the evolution over time of key features (environmental damage costs, learning, technological progress, number of signatories, economic development), when this evolution depends on the players' joint strategies. In practice, increasing foresight translates into multidimensional models.