2026/01/20 by Michail Anthropelos, Constantinos Kardaras, Constantinos Stefanakis · 1 voice
Economics, Econometrics and Finance · #q-fin.MF
arxiv published 2026/01/20 · arxiv updated 2026/01/22
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.