An Explicit Solution for the Problem of Optimal Investment with Random Endowment
Portfolio Management
2025-06-26 v1
Abstract
We consider the problem of optimal investment with random endowment in a Black--Scholes market for an agent with constant relative risk aversion. Using duality arguments, we derive an explicit expression for the optimal trading strategy, which can be decomposed into the optimal strategy in the absence of a random endowment and an additive shift term whose magnitude depends linearly on the endowment-to-wealth ratio and exponentially on time to maturity.
Keywords
Cite
@article{arxiv.2506.20506,
title = {An Explicit Solution for the Problem of Optimal Investment with Random Endowment},
author = {Michael Donisch and Christoph Knochenhauer},
journal= {arXiv preprint arXiv:2506.20506},
year = {2025}
}