Minimizing Expected Loss Of Hedging In Incomplete And Constrained Markets

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摘要：

We study the problem of minimizing the expected discounted loss E[e -(int 0Tr(u)du)(C-X x,pi(T)) +] when hedging a liability C at time t=T, using an admissible portfolio strategy pi(middot) and starting with initial wealth x. The existence of an optimal solution is established in the context of continuous-time Ito process incomplete market models, by studying an appropriate dual problem. It is shown that the optimal strategy is of the form of a knock-out option with payoff C, where the ldquodomain of the knock-outrdquo depends on the value of the optimal dual variable. We also discuss a dynamic measure for the risk associated with the liability C, defined as the supremum over different scenarios of the minimal expected loss of hedging C

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Theoretical or Mathematical/ constraint theory investment optimisation risk management/ expected loss hedging incomplete constrained markets portfolio optimal strategy risk measures finance optimisation/ C1290D Systems theory applications in economics and business C1180 Optimisation techniques E0210G Optimisation E0220 Economics E1540 Systems theory applications