$α$-robust utility maximization with intractable claims: A quantile optimization approach
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913007615868928 |
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| author | Chen, Xinyu Xu, Zuo Quan |
| author_facet | Chen, Xinyu Xu, Zuo Quan |
| contents | This paper studies an $α$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market returns. The $α$-robust criterion interpolates between worst-case ($α=0$) and best-case ($α=1$) evaluations, generalizing both extremes through a continuous ambiguity attitude parameter. For weighted exponential utilities, we establish via rearrangement inequalities and comonotonicity theory that the $α$-robust risk measure is law-invariant, depending only on marginal distributions. This transforms the dynamic stochastic control problem into a concave static quantile optimization over a convex domain. We derive optimality conditions via calculus of variations and characterize the optimal quantile as the solution to a two-dimensional first-order ordinary differential equation system, which is a system of variational inequalities with mixed boundary conditions, enabling numerical solution. Our framework naturally accommodates additional risk constraints such as Value-at-Risk and Expected Shortfall. Numerical experiments reveal how ambiguity attitude, market conditions, and claim characteristics interact to shape optimal payoffs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_04649 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $α$-robust utility maximization with intractable claims: A quantile optimization approach Chen, Xinyu Xu, Zuo Quan Portfolio Management Optimization and Control Mathematical Finance 91B28, 91G10, 49N90, 35Q93 This paper studies an $α$-robust utility maximization problem where an investor faces an intractable claim -- an exogenous contingent claim with known marginal distribution but unspecified dependence structure with financial market returns. The $α$-robust criterion interpolates between worst-case ($α=0$) and best-case ($α=1$) evaluations, generalizing both extremes through a continuous ambiguity attitude parameter. For weighted exponential utilities, we establish via rearrangement inequalities and comonotonicity theory that the $α$-robust risk measure is law-invariant, depending only on marginal distributions. This transforms the dynamic stochastic control problem into a concave static quantile optimization over a convex domain. We derive optimality conditions via calculus of variations and characterize the optimal quantile as the solution to a two-dimensional first-order ordinary differential equation system, which is a system of variational inequalities with mixed boundary conditions, enabling numerical solution. Our framework naturally accommodates additional risk constraints such as Value-at-Risk and Expected Shortfall. Numerical experiments reveal how ambiguity attitude, market conditions, and claim characteristics interact to shape optimal payoffs. |
| title | $α$-robust utility maximization with intractable claims: A quantile optimization approach |
| topic | Portfolio Management Optimization and Control Mathematical Finance 91B28, 91G10, 49N90, 35Q93 |
| url | https://arxiv.org/abs/2604.04649 |