We study the generalized composite pure and randomized hypothesis testing problems. In addition to characterizing the corresponding optimal tests, we examine the conditions under which these two hypothesis testing problems are equivalent, and provide counterexamples when they are not. This analysis is useful for portfolio optimization problems that maximize some success probability given a fixed initial capital. The corresponding dual is related to a pure hypothesis testing problem which may or may not coincide with the randomized hypothesis testing problem . Our framework is applicable to both complete and incomplete market settings .
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be formulated as a composite pure hypothesis testing problem . We analyze the connection between this pure testing problem and its randomized counterpart, and from latter we derive a dual representation for the maximal outperformance probability. Moreover, in a complete market setting, we provide a closed-form solution to the problem of beating a leveraged exchange traded fund. For a general benchmark under an incomplete stochastic factor model, we provide the Hamilton-Jacobi-Bellman PDE characterization for the maximal outperformance probability .
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generalized composite pure and randomized hypothesis testing problems. In addition to characterizing the corresponding optimal tests, we examine the conditions under which these two hypothesis testing problems are equivalent, and provide counterexamples when they are not. This analysis is useful for portfolio optimization problems that maximize some success probability given a
portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a
R
The corresponding dual is related to a
Under a general incomplete market framework, this stochastic control problem can be formulated as a composite
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which may or may not coincide with the randomized hypothesis testing problem . Our framework is applicable to both complete and incomplete market settings
. We analyze the connection between this pure testing problem and its randomized counterpart, and from latter we derive a dual representation for the maximal outperformance probability. Moreover, in a complete market setting, we provide a closed-form solution to the problem of beating a leveraged exchange traded fund. For a general benchmark under an incomplete stochastic factor model, we provide the Hamilton-Jacobi-Bellman PDE characterization for the maximal outperformance probability