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Log-optimality with small liability stream

Author

Listed:
  • Michail Anthropelos
  • Constantinos Kardaras
  • Constantinos Stefanakis

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 $\epsilon$, 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. $\epsilon$. 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.

Suggested Citation

  • Michail Anthropelos & Constantinos Kardaras & Constantinos Stefanakis, 2026. "Log-optimality with small liability stream," Papers 2601.14139, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2601.14139
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    References listed on IDEAS

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    3. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
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