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Stochastic Optimal Control Formulati...

Kwon, Daihyun.

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Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling./
Author:	Kwon, Daihyun.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	98 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-05, Section: B.
Contained By:	Dissertations Abstracts International85-05B.
Subject:	Partial differential equations. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30673738
ISBN:	9798380714365

Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.
Kwon, Daihyun.

Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 98 p.

Source: Dissertations Abstracts International, Volume: 85-05, Section: B.

Thesis (Ph.D.)--North Carolina State University, 2023.

In this thesis, we explore the portfolio selection problem of maximizing utility and consumption for incomplete market models. Specifically, we analyze the optimal policy for Heston's stochastic volatility model using Hamilton-Jacobi-Bellman (HJB) theory, with the objective of developing solution methods to construct an explicit formula. To this end, we derive an explicit Merton-like optimal policy for the case of power utility by using a separable variable method to the corresponding HJB equation for Heston's model. Additionally, we extend our analysis of Heston's model by modeling the Market Price of Risk (MPR) as an independent stochastic process, leading to further insights into portfolio selection. Moving beyond, we then extend our analysis and methods to benchmark optimization problems in mathematical finance. To tackle state constraint stochastic optimal control problems, we adapt three approaches: 1) transformation of the state process with benchmark constraints for feasible optimal control problems, 2) formulation of the constraint into a cost functional as a violation measure, and 3) a PDE approach based on HJB theory for the general state constraint stochastic optimal control problems. Lastly, we end our presentation with a discussion of the extension of Merton theory and jump process modeling in finance. We provide a brief introduction to the jump process used in financial modeling, and then examine selected problems, such as the two-player Nash game and the optimal exit time problem.

ISBN: 9798380714365Subjects--Topical Terms:

2180177
Partial differential equations.

Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.
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245 1 0 $a Stochastic Optimal Control Formulations in Finance: Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.
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500 $a Source: Dissertations Abstracts International, Volume: 85-05, Section: B.
500 $a Advisor: Medhin, Negash;Li, Zhilin;Pang, Tao;Ito, Kazufumi.
502 $a Thesis (Ph.D.)--North Carolina State University, 2023.
520 $a In this thesis, we explore the portfolio selection problem of maximizing utility and consumption for incomplete market models. Specifically, we analyze the optimal policy for Heston's stochastic volatility model using Hamilton-Jacobi-Bellman (HJB) theory, with the objective of developing solution methods to construct an explicit formula. To this end, we derive an explicit Merton-like optimal policy for the case of power utility by using a separable variable method to the corresponding HJB equation for Heston's model. Additionally, we extend our analysis of Heston's model by modeling the Market Price of Risk (MPR) as an independent stochastic process, leading to further insights into portfolio selection. Moving beyond, we then extend our analysis and methods to benchmark optimization problems in mathematical finance. To tackle state constraint stochastic optimal control problems, we adapt three approaches: 1) transformation of the state process with benchmark constraints for feasible optimal control problems, 2) formulation of the constraint into a cost functional as a violation measure, and 3) a PDE approach based on HJB theory for the general state constraint stochastic optimal control problems. Lastly, we end our presentation with a discussion of the extension of Merton theory and jump process modeling in finance. We provide a brief introduction to the jump process used in financial modeling, and then examine selected problems, such as the two-player Nash game and the optimal exit time problem.
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