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<p>We investigate an expected utility maximisation problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model ℙ with an adverse choice from a Wasserstein ball of radius <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_558_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> <EquationSource Format="TEX">$k$</EquationSource> </InlineEquation> around&#xa0;ℙ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimisation problem. We show that solutions converge to a strategy with minimal norm when uncertainty becomes large, i.e., when the radius <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="780_2025_558_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> <EquationSource Format="TEX">$k$</EquationSource> </InlineEquation> tends to infinity.</p>

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Strategies with minimal norm are optimal for expected utility maximisation under high model ambiguity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月6日

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  • Laurence Carassus,
  • Johannes Wiesel

摘要

We investigate an expected utility maximisation problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model ℙ with an adverse choice from a Wasserstein ball of radius k $k$ around ℙ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimisation problem. We show that solutions converge to a strategy with minimal norm when uncertainty becomes large, i.e., when the radius k $k$ tends to infinity.