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

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Stochastic Optimal Control Formulations in Finance :/
其他題名:	Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.
作者:	Kwon, Daihyun.
面頁冊數:	1 online resource (98 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-05, Section: B.
Contained By:	Dissertations Abstracts International85-05B.
標題:	Systems science. -
電子資源:	click for full text (PQDT)
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. - 1 online resource (98 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380714365Subjects--Topical Terms:

1148479
Systems science.
Index Terms--Genre/Form:

554714
Electronic books.

Stochastic Optimal Control Formulations in Finance : = Extension of Merton Theory, Benchmark Problems, and Jump Process Modeling.
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504 $a Includes bibliographical references
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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