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Permanent link (DOI): https://doi.org/10.7939/R3QW70

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Stochastic Control in Optimal Insurance and Investment with Regime Switching Open Access

Descriptions

Other title
Subject/Keyword
Economic Analysis
Stochastic Control
Financial Crisis
Risk Management
Optimal Insurance
Hamilton-Jacobi-Bellman equations
Optimal Consumption and Investment
Regime Switching
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Zou, Bin
Supervisor and department
Cadenillas, Abel (Mathematical and Statistical Sciences)
Examining committee member and department
Galvani, Valentina (Economics)
Melnikov, Alexander (Mathematical and Statistical Sciences)
Frei, Christoph (Mathematical and Statistical Sciences)
Schmuland, Byron (Mathematical and Statistical Sciences)
Cadenillas, Abel (Mathematical and Statistical Sciences)
Aguerrevere, Felipe (Finance and Statistical Analysis)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Finance
Date accepted
2014-12-16T15:35:13Z
Graduation date
2015-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Motivated by the financial crisis of 2007-2009 and the increasing demand for portfolio and risk management, we study optimal insurance and investment problems with regime switching in this thesis. We incorporate an insurable risk into the classical consumption and investment framework and consider an investor who wants to select optimal consumption, investment and insurance policies in a regime switching economy. We allow not only the financial market but also the insurable risk to depend on the regime of the economy. The objective of the investor is to maximize his/her expected total discounted utility of consumption over an infinite time horizon. For the case of hyperbolic absolute risk aversion (HARA) utility functions, we obtain the first explicit solutions for simultaneous optimal consumption, investment and insurance problems when there is regime switching. Next we consider an insurer who wants to maximize his/her expected utility of terminal wealth by selecting optimal investment and risk control policies. The insurer's risk is modeled by a jump-diffusion process and is negatively correlated with the capital gains in the financial market. In the case of no regime switching in the economy, we apply the martingale approach to obtain optimal policies for HARA utility functions, constant absolute risk aversion (CARA) utility functions, and quadratic utility functions. When there is regime switching in the economy, we apply dynamic programming to derive the associated Hamilton-Jacobi-Bellman (HJB) equation. Optimal investment and risk control policies are then obtained in explicit forms by solving the HJB equation. We provide economic analyses for all optimal control problems considered in this thesis. We study how optimal policies are affected by the economic conditions, the financial and insurance markets, and investor's risk preference.
Language
English
DOI
doi:10.7939/R3QW70
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Zou, B., and Cadenillas, A., 2014. Explicit solutions of optimal consumption, investment and insurance problems with regime switching. Insurance: Mathematics and Economics 58, 159-167.Zou, B., and Cadenillas, A., 2014. Optimal investment and risk control policies for an insurer: expected utility maximization. Insurance: Mathematics and Economics 58, 57-67.

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