Application of conditional set theory to stochastic optimization

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We will study stochastic optimization problems by means of the conditional set theory. Conditional set theory allows to deal with local structures which, for instance, arise in dynamic and robust financial market models. The method is developed in [33] as an extension of the results in topological L0-modules, initiated in [35]. Conditional set theory has already been successfully applied to conditional risk measure theory, decision theory, equilibrium pricing and backward stochastic differential equations. In this proposal we suggest a work programme for applications to stochastic optimization problems which are motivated by equilibrium models and control problems in financial markets with volatility uncertainty.