Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911155911393280 |
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| author | Chong, Wing Fung Liang, Gechun |
| author_facet | Chong, Wing Fung Liang, Gechun |
| contents | This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {Therein, w}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {analysis} for forward investment and consumption under model uncertainty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach Chong, Wing Fung Liang, Gechun Portfolio Management Mathematical Finance 60H30, 91G10 This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {Therein, w}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {analysis} for forward investment and consumption under model uncertainty. |
| title | Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach |
| topic | Portfolio Management Mathematical Finance 60H30, 91G10 |
| url | https://arxiv.org/abs/2410.01378 |