We consider the problem of active portfolio management where a loss-averse and/or gain-seeking investor aims to outperform a benchmark strategy's risk profile while not deviating too much from it. Specifically, an investor considers alternative strategies that co-move with the benchmark and whose terminal wealth lies within a Wasserstein ball surrounding  it. The investor then chooses the alternative strategy that minimises their personal risk preferences, modelled in terms of a distortion risk measure  . In a general  market model, we prove that an optimal dynamic strategy exists and is unique, and provide its characterisation through the notion of isotonic projections.  Finally, we illustrate how investors with different  risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped distortion risk measures , and lower- and upper-tail  risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving some aspects of the benchmark .
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth . In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections. We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped , and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure .
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consider
study
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a loss-averse and/or gain-seeking
an
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much
far
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that co-move with the benchmark and
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lies
lie
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a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to
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their personal risk preferences, modelled in terms of
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of terminal wealth
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(complete)
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is unique, and
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We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models.
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copula and
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distortion risk measures
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distortion
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some aspects of the benchmark
the benchmark's structure