Complete markets do not allow free cash flow streams
In this short note we prove a conjecture posed in Cui et al. (Math Finance 22:346–378, 2012): Dynamic mean–variance problems in arbitrage-free, complete financial markets do not allow free cash flows. Moreover, we show by investigating a benchmark problem that this effect is due to the performance criterion and not due to the time inconsistency of the strategy.
KeywordsMean–variance problem Time-inconsistency Market completeness Benchmark problem
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