Optimal investment, valuation and hedging under model ambiguity
<p>In this thesis, we study several utility maximisation problems under model uncertainty, involving optimal investment, valuation and hedging.</p> <p>We first derived martingale distortion representations for classical utility maximisation problems in a non-Markovian stochastic f...
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| Format: | Thesis |
| Language: | English |
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2022
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| _version_ | 1826309216771506176 |
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| author | Ye, J |
| author2 | Monoyios, M |
| author_facet | Monoyios, M Ye, J |
| author_sort | Ye, J |
| collection | OXFORD |
| description | <p>In this thesis, we study several utility maximisation problems under model uncertainty, involving optimal investment, valuation and hedging.</p>
<p>We first derived martingale distortion representations for classical utility maximisation problems in a non-Markovian stochastic factor model, with power, logarithmic and exponential utilities.</p>
<p>We then study multiple priors power utility maximisation problems when the reference model is a non-Markovian stochastic factor model, and derive a BSDE representation of the value process, optimal strategy and least favourable model.</p>
<p>We also study a variational preferences logarithmic utility maximisation problem when the reference model is a non-Markovian stochastic factor model, and when the plausible models are penalised by an additive entropic penalty function. The robust problem is transferred to a classical utility maximisation problem with a power utility whose risk aversion is dependent on the model ambiguity aversion parameter. We then fully solve the robust problem and perform numerical tests comparing several classical and robust strategies for a Stein-Stein stochastic volatility model and for a Heston model.</p>
<p>Finally, we study robust exponential valuation and hedging problems in a basis risk model, using both the multiple priors approach and the variational preferences approach with a multiplicative penalty function. Specialising to a constant parameter basis risk model, the robust problems admit explicit or approximate solutions, thus we are able to conduct large-scale simulation based tests on performances of various pricing and hedging strategies.</p> |
| first_indexed | 2024-03-07T07:30:49Z |
| format | Thesis |
| id | oxford-uuid:b22f1122-c065-4a49-994c-8b72e7e3df08 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:30:49Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | oxford-uuid:b22f1122-c065-4a49-994c-8b72e7e3df082023-01-20T09:28:51ZOptimal investment, valuation and hedging under model ambiguityThesishttp://purl.org/coar/resource_type/c_db06uuid:b22f1122-c065-4a49-994c-8b72e7e3df08financial mathematicsEnglishHyrax Deposit2022Ye, JMonoyios, M<p>In this thesis, we study several utility maximisation problems under model uncertainty, involving optimal investment, valuation and hedging.</p> <p>We first derived martingale distortion representations for classical utility maximisation problems in a non-Markovian stochastic factor model, with power, logarithmic and exponential utilities.</p> <p>We then study multiple priors power utility maximisation problems when the reference model is a non-Markovian stochastic factor model, and derive a BSDE representation of the value process, optimal strategy and least favourable model.</p> <p>We also study a variational preferences logarithmic utility maximisation problem when the reference model is a non-Markovian stochastic factor model, and when the plausible models are penalised by an additive entropic penalty function. The robust problem is transferred to a classical utility maximisation problem with a power utility whose risk aversion is dependent on the model ambiguity aversion parameter. We then fully solve the robust problem and perform numerical tests comparing several classical and robust strategies for a Stein-Stein stochastic volatility model and for a Heston model.</p> <p>Finally, we study robust exponential valuation and hedging problems in a basis risk model, using both the multiple priors approach and the variational preferences approach with a multiplicative penalty function. Specialising to a constant parameter basis risk model, the robust problems admit explicit or approximate solutions, thus we are able to conduct large-scale simulation based tests on performances of various pricing and hedging strategies.</p> |
| spellingShingle | financial mathematics Ye, J Optimal investment, valuation and hedging under model ambiguity |
| title | Optimal investment, valuation and hedging under model ambiguity |
| title_full | Optimal investment, valuation and hedging under model ambiguity |
| title_fullStr | Optimal investment, valuation and hedging under model ambiguity |
| title_full_unstemmed | Optimal investment, valuation and hedging under model ambiguity |
| title_short | Optimal investment, valuation and hedging under model ambiguity |
| title_sort | optimal investment valuation and hedging under model ambiguity |
| topic | financial mathematics |
| work_keys_str_mv | AT yej optimalinvestmentvaluationandhedgingundermodelambiguity |