An Explicit Solution for the Problem of Optimal Investment with Random Endowment
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913912320950272 |
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| author | Donisch, Michael Knochenhauer, Christoph |
| author_facet | Donisch, Michael Knochenhauer, Christoph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Explicit Solution for the Problem of Optimal Investment with Random Endowment Donisch, Michael Knochenhauer, Christoph Portfolio Management 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. |
| title | An Explicit Solution for the Problem of Optimal Investment with Random Endowment |
| topic | Portfolio Management |
| url | https://arxiv.org/abs/2506.20506 |