Stochastic control and first passage time probabilities in finance

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Many complex dynamic systems are modeled successfully by stochastic processes (ex.: stochastic differential equations) and this is particularly the case for stock markets. In a financial market, an investor might seek to establish a dynamic strategy allowing him to optimize a certain function of the expected terminal wealth (ex.: miminizing risk functions, maximizing expected utility ...). With this in mind, he must base his decisions on a continuously updated flow of information without being able to exactly predict future market fluctuations. This research program aims at developing innovative investment strategies under realistic constraints, either imposed by the investor or enforced by the market, while considering market models with (possibly unbounded) stochastic parameters. This can be achieved with breakthroughs in finding new optimal solutions to general stochastic control problems using more recent results in BSDE (backward stochastic differential equations) theory. Furthermore, by striving for solutions to more intricate first-passage time problems, this will ultimately lead to cutting-edge hybrid strategies where stopping time rules are incorporated as a safeguard against financial distress for cautious investors which main focus is their goal-achieving probability.