This project has three main objectives: (1) exploring in depth the applications of large deviations in finance; (2) understanding in which directions the theory of large deviations can be advanced in view of financial applications; and (3) developing the theory in these directions. Applications will include: (1) long term investment problems, where asymptotics of optimization problems will be analyzed and compared with risk-sensitive control problems and turnpike theorems; (2) asymmetric information models, where the dependence of the economic value of additional information on risk-aversion will be studied; and (3) Monte Carlo methods, where asymptotically optimal techniques will be devised for pricing derivatives. In all these problems, it is expected that a crucial role will be played by infinite-dimensional results in large deviations.
This research will employ innovative mathematical tools to: (1) analyze the welfare effect of predictable components of asset prices for long-term investors across different levels of risk-aversion and different information sets; (2) develop high-performance Monte Carlo algorithms for pricing complex financial derivatives on equities and corporate bonds; and (3) further advance the theory of large deviations, which has a wide scope of applications, spanning manufacturing engineering, finance, information theory and physics among others.
