Some Stochastic Optimization Problems in Reinsurance and Insurance
Loading...
Date
2021-01-12
Authors
Cao, Jingyi
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Insurance, which hedges against the risk of a contingent loss, is an indispensable risk management tool for both institutions and individuals. Reinsurance, namely, a form of insurance accessible to insurers, helps limit the liability of an insurer on certain set of risks and protect against catastrophic events, while various insurance products are available for individuals to cover uncertain losses from almost every aspect of their daily life. This thesis focuses on dynamically controlling the utilities of decision makers by imposing various controls, including reinsurance for insurers, and life annuity and term life insurance for individuals, either analytically or numerically.
Utilizing (re)insurance to attain certain objectives has long been a central focus in the actuarial science literature. This thesis aims at making contributions in the existing literature by applying models that are more in line with reality, both in regard to the underlying dynamic models and control variables.
In Chapter 3, we study the optimal reinsurance-investment strategy for dynamic contagion claims. Such a claim process no longer possesses the stationary and independent increment property, and can capture contagion due to endogenous (self-exciting) and exogenous (externally-exciting) factors. Adopting the time-consistent mean-variance criterion, we analytically solve for the equilibrium strategies and analyze the impact of some contagion factors on the resulting optimal reinsurance strategies.
Chapter 4 models the basic surplus process as a spectrally negative Lévy process, and focuses on the partial information of the unobservable stock return rate to look into the optimal reinsurance-investment problem under the time-consistent mean-variance criterion. Analytical solutions are obtained by solving an extended HJB equation, and hedging demand due to partial information is carefully studied.
Chapter 5 is devoted to the study of the optimal allocation of life annuity, term life insurance and consumption for an individual under a general force of mortality. In our setup, an individual's decision of life annuity, term life insurance and consumption are allowed to depend on the current wealth, existing life annuity and existing term life insurance, and realistic lump-sum purchases are considered. Assuming a CRRA preference, a penalty method is applied to numerically solve for the optimal allocations of wealth in life annuity, term life insurance and consumption.
To ensure that the thesis flows smoothly, Chapter 1 introduces the background literature and main motivations of this thesis. Chapter 2 is devoted to mathematical preliminaries for the latter chapters. Finally, Chapter 6 concludes the thesis with potential directions for future research.
Description
Keywords
reinsurance, life annuity, term life insurance, contagion claims, general force of mortality
LC Keywords
Reinsurance, Reinsurance claims, Insurance, Insurance claims, Term life insurance policies, Annuities