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We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems...
We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.
Asymmetric or partial information in financial markets may be
represented by different filtrations. We consider the case of a
larger filtration F – the natural filtration of the
“model world” – and a subfiltration that
represents the information available to an agent in the “real
world”. Given a price system on the larger filtration that is
represented by a martingale measure Q and an associated numeraire S, we show that there is a canonical and nontrivial numeraire Ŝ such that the price system...
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