Conditioned stochastic differential equations: theory, examples and application to finance

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Duality theory for optimal investments under model uncertainty (2005, background): “Another example for which (1) is not satisfied is provided by the case of “weak information”, where Q consists of all measures Q P under which a given random variable has a fixed distribution; see Plachky and Rüschendorf [17] and Baudoin [2].”
Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, methodology): “In solving this problem, he introduced a transformation of the Wiener process, now referred to as Doob’s h-transform, which was later adapted under the same name to deal with other conditionings of stochastic processes, including the Brownian bridge [3], Gaussian bridges [4–6], and the Schrödinger b”
Dynamic Markov bridges motivated by models of insider trading (2011, background): “with the initial condition X0 = 0, which satisfies all the properties stated inC1-C3 (see Proposition 37 in [5] for a proof of this and other related results.”
Robust Preferences and Robust Portfolio Choice (2009, methodology): “The robust utility maximization problem for this set Q was studied by BAUDOIN [2002], who coined the terminology “weak information”.”
Risk Measures and Robust Optimization Problems (2006, methodology): “Baudoin, F. Conditioned stochastic differential equations: theory, examples and application to finance.”