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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.14139 |
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| _version_ | 1866911391425757184 |
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| author | Anthropelos, Michail Kardaras, Constantinos Stefanakis, Constantinos |
| author_facet | Anthropelos, Michail Kardaras, Constantinos Stefanakis, Constantinos |
| contents | In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality techniques, we derive the fourth-order expansion of the primal value function with respect to the units $ε$, held in the non-traded endowment. In turn, this lays the foundation for expanding the optimal wealth process, in this context, up to second order w.r.t. $ε$. The key processes underpinning the aforementioned results are given in terms of Kunita-Watanabe projections, mirroring the case of lower order expansions of similar nature. Both the case of finite and infinite horizons are treated in a unified manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14139 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-optimality with small liability stream Anthropelos, Michail Kardaras, Constantinos Stefanakis, Constantinos Mathematical Finance 91B70 (Primary), 60H30, 41A10 (Secondary) In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality techniques, we derive the fourth-order expansion of the primal value function with respect to the units $ε$, held in the non-traded endowment. In turn, this lays the foundation for expanding the optimal wealth process, in this context, up to second order w.r.t. $ε$. The key processes underpinning the aforementioned results are given in terms of Kunita-Watanabe projections, mirroring the case of lower order expansions of similar nature. Both the case of finite and infinite horizons are treated in a unified manner. |
| title | Log-optimality with small liability stream |
| topic | Mathematical Finance 91B70 (Primary), 60H30, 41A10 (Secondary) |
| url | https://arxiv.org/abs/2601.14139 |