Mathematical Sciences: Stochastic Control and Applications in Mathematical Economics

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Research in stochastic analysis and control, with special emphasis on mathematical economics and on problems of singular control and optimal stopping. Particular topics include: (i) a detailed study of single-agent portfolio/consumption problems with very general market models and utility functions, using techniques from stochastic analysis; (ii) the associated treatment of equilibrium problems for an economy with several agents, whose joint optimal actions determine the prices of traded commodites by "clearing" the markets; (iii) a new approach to optimal stopping using the theory of balayage semimartingales, and the discussion of its ramifications for the reflection problem of Skorohod and for singular stochastic control; and (iv) a study of integral functionals for diffusion processes and semimartingales.