Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866913190459211776 |
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| author | Luxenberg, Eric Schiele, Philipp Boyd, Stephen |
| author_facet | Luxenberg, Eric Schiele, Philipp Boyd, Stephen |
| contents | We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. The first term is the composition of a convex function with concave arguments and the second term a composition of a convex function with convex arguments. This structure allows us to derive a global lower bound, or minorant, on the CPT utility, which we can use in a minorization-maximization (MM) algorithm for maximizing CPT utility. We further show that the problem is amenable to a simple convex-concave (CC) procedure which iteratively maximizes a local approximation. Both of these methods can handle small and medium size problems, and complex (but convex) portfolio constraints. We also describe a simpler method that scales to larger problems, but handles only simple portfolio constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03461 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization Luxenberg, Eric Schiele, Philipp Boyd, Stephen Optimization and Control Portfolio Management G.1.6 We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. The first term is the composition of a convex function with concave arguments and the second term a composition of a convex function with convex arguments. This structure allows us to derive a global lower bound, or minorant, on the CPT utility, which we can use in a minorization-maximization (MM) algorithm for maximizing CPT utility. We further show that the problem is amenable to a simple convex-concave (CC) procedure which iteratively maximizes a local approximation. Both of these methods can handle small and medium size problems, and complex (but convex) portfolio constraints. We also describe a simpler method that scales to larger problems, but handles only simple portfolio constraints. |
| title | Portfolio Optimization with Cumulative Prospect Theory Utility via Convex Optimization |
| topic | Optimization and Control Portfolio Management G.1.6 |
| url | https://arxiv.org/abs/2209.03461 |