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- Document type:
- Masterarbeit
- Author(s):
- Hron, Peter
- Title:
- Dynamic Portfolio Optimization for Time-Inconsistent Models
- Abstract:
- In this thesis, we study the optimizers of the mean-variance objective using the framework of optimal control, with particular focus on the handling of the time-inconsistency (a violation of the dynamic programming principle) that stems from the non-linearity of the variance term. Due to the absence of the dynamic programming principle, the notion of optimality for control laws is ambiguous, and we discuss several views of optimality: static optimality (Bajeux-Besnainou & Portait, 1998; Li & Zhou, 2000), dynamic optimality (Pedersen & Peskir, 2017), and game-theoretic optimality (Basak & Chabakauri, 2008; Björk & Murgoci, 2014). For the model setting of a Black-Scholes-type stochastic differential equation, we utilize their results in finding optimal control laws for the mean-variance objective, and discuss the difference that stem from following the various views of optimality. The main theoretical result is the derivation of the corresponding control laws, using the Hamilton-Jacobi-Bellman approach of stochastic control. Further, we shortly focus on the generalization of the model setting to a more general time-inconsistent functional with a drift-diffusion state process and derive the corresponding Hamilton-Jacobi-Bellman result along with a verification theorem, verifying a result of Björk, Khapko, Murgoci, 2014.
- Advisor:
- Prof. Dr. Rudi Zagst
- Referee:
- Prof. Dr. Rudi Zagst
- Year:
- 2023
- University:
- Technische Universität München
- Commencing Date:
- 15.11.2023
- End of processing:
- 12.12.2023
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