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Theory of Mathematical Optimization for Delegated Portfolio Management


Tao, Zijian (2022) Theory of Mathematical Optimization for Delegated Portfolio Management. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/km2b-er60.


We study the optimization problem of finding closed convex sets Γ ⊆ Rd containing the origin that minimize F(Γ) = ∑i=1k wi | θi/2 - pΓi) | 2, where w1, ..., wk > 0, θ1, ..., θk in Rd are given, and pΓi) are the closest points in Γ to θi, i = 1, ..., k. This problem is motivated by the topic of delegated portfolio management in finance. In Chapter 2, we will explore this connection. To approach the problem, we first prove existence of a solution for the general problem. To further study properties of the solution, we next introduce the semidefinite programming relaxation, for which we have a first-order characterization of optimality. We then explore the question of exactness of this relaxation, which turns out to be equivalent to the notion of localizability: the shape optimization problem embedded in higher dimensions must have solutions in the original dimension. Finally, we present special cases for which localizability holds.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:mathematical finance, screening, mathematical optimization, semidefinite programming
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics, 2021.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Cvitanić, Jakša
Thesis Committee:
  • Tamuz, Omer (chair)
  • Cvitanić, Jakša
  • Makarov, Nikolai G.
  • Sandomirskiy, Fedor
Defense Date:19 May 2022
Record Number:CaltechTHESIS:05272022-034901698
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14634
Deposited By: Zijian Tao
Deposited On:02 Jun 2022 19:57
Last Modified:03 Aug 2022 21:14

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