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An Explicit Solution for the Problem of Optimal Investment with Random Endowment

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  • Michael Donisch
  • Christoph Knochenhauer

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.

Suggested Citation

  • Michael Donisch & Christoph Knochenhauer, 2025. "An Explicit Solution for the Problem of Optimal Investment with Random Endowment," Papers 2506.20506, arXiv.org.
    • Handle: RePEc:arx:papers:2506.20506
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    File URL: http://arxiv.org/pdf/2506.20506
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    References listed on IDEAS

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    1. Oleksii Mostovyi, 2017. "Optimal Investment With Intermediate Consumption And Random Endowment," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 96-114, January.
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