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arXiv · 2601.14139

Log-optimality with small liability stream

Michail Anthropelos·Constantinos Kardaras·Constantinos Stefanakis
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Abstract

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.

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Michail Anthropelos, Constantinos Kardaras, Constantinos Stefanakis. 2026-01-22. Log-optimality with small liability stream. https://arxiv.org/abs/2601.14139

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