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postgraduate thesis: Optimal reinsurance: a contemporary perspective
Title  Optimal reinsurance: a contemporary perspective 

Authors  
Advisors  Advisor(s):Yung, SP 
Issue Date  2012 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Sung, K. J. [宋家俊]. (2012). Optimal reinsurance : a contemporary perspective. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4775303 
Abstract  In recent years, general risk measures have played an important role in risk management
in both finance and insurance industry. As a consequence, there is an
increasing number of research on optimal reinsurance problems using risk measures
as yard sticks beyond the classical expected utility framework.
In this thesis, the stoploss reinsurance is first shown to be an optimal contract
under lawinvariant convex risk measures via a new simple geometric argument.
This similar approach is then used to tackle the same optimal reinsurance problem
under Value at Risk and Conditional Tail Expectation; it is interesting to note
that, instead of stoploss reinsurances, insurance layers serve as the optimal solution
in these cases. These two results hint that lawinvariant convex risk measure
may be better and more robust to expected larger claims than Value at Risk and
Conditional Tail Expectation even though they are more commonly used.
In addition, the problem of optimal reinsurance design for a basket of n insurable
risks is studied. Without assuming any particular dependence structure, a
minimax optimal reinsurance decision formulation for the problem has been successfully
proposed. To solve it, the least favorable dependence structure is first
identified, and then the stoploss reinsurances are shown to minimize a general
lawinvariant convex risk measure of the total retained risk. Sufficient condition
for ordering the optimal deductibles are also obtained.
Next, a PrincipalAgent model is adopted to describe a monopolistic reinsurance
market with adverse selection. Under the asymmetry of information, the reinsurer
(the principal) aims to maximize the average profit by selling a tailormade reinsurance
to every insurer (agent) from a (huge) family with hidden characteristics.
In regard to Basel Capital Accord, each insurer uses Value at Risk as the risk assessment,
and also takes the right to choose different risk tolerances. By utilizing
the special features of insurance layers, their optimality as the firstbest strategy
over all feasible reinsurances is proved. Also, the same optimal reinsurance
screening problem is studied under other subclass of reinsurances: (i) deductible
contracts; (ii) quotashare reinsurances; and (iii) reinsurance contracts with convex
indemnity, with the aid of indirect utility functions. In particular, the optimal
indirect utility function is shown to be of the stoploss form under both classes
(i) and (ii); while on the other hand, its nonstoploss nature under class (iii) is
revealed.
Lastly, a class of nonzerosum stochastic differential reinsurance games between
two insurance companies is studied. Each insurance company is assumed to maximize
the difference of the opponent’s terminal surplus from that of its own by
properly arranging its reinsurance schedule. The surplus process of each insurance
company is modeled by a mixed regimeswitching CramerLundberg approximation.
It is a diffusion risk process with coefficients being modulated by both
a continuoustime finitestate Markov Chain and another diffusion process; and
correlations among these surplus processes are allowed. In contrast to the traditional
HJB approach, BSDE method is used and an explicit Nash equilibrium is
derived. 
Degree  Master of Philosophy 
Subject  Reinsurance  Mathematics. Risk (Insurance)  Mathematics. 
Dept/Program  Mathematics 
Persistent Identifier  http://hdl.handle.net/10722/174483 
HKU Library Item ID  b4775303 
DC Field  Value  Language 

dc.contributor.advisor  Yung, SP   
dc.contributor.author  Sung, Kachun, Joseph.   
dc.contributor.author  宋家俊.   
dc.date.issued  2012   
dc.identifier.citation  Sung, K. J. [宋家俊]. (2012). Optimal reinsurance : a contemporary perspective. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4775303   
dc.identifier.uri  http://hdl.handle.net/10722/174483   
dc.description.abstract  In recent years, general risk measures have played an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance problems using risk measures as yard sticks beyond the classical expected utility framework. In this thesis, the stoploss reinsurance is first shown to be an optimal contract under lawinvariant convex risk measures via a new simple geometric argument. This similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stoploss reinsurances, insurance layers serve as the optimal solution in these cases. These two results hint that lawinvariant convex risk measure may be better and more robust to expected larger claims than Value at Risk and Conditional Tail Expectation even though they are more commonly used. In addition, the problem of optimal reinsurance design for a basket of n insurable risks is studied. Without assuming any particular dependence structure, a minimax optimal reinsurance decision formulation for the problem has been successfully proposed. To solve it, the least favorable dependence structure is first identified, and then the stoploss reinsurances are shown to minimize a general lawinvariant convex risk measure of the total retained risk. Sufficient condition for ordering the optimal deductibles are also obtained. Next, a PrincipalAgent model is adopted to describe a monopolistic reinsurance market with adverse selection. Under the asymmetry of information, the reinsurer (the principal) aims to maximize the average profit by selling a tailormade reinsurance to every insurer (agent) from a (huge) family with hidden characteristics. In regard to Basel Capital Accord, each insurer uses Value at Risk as the risk assessment, and also takes the right to choose different risk tolerances. By utilizing the special features of insurance layers, their optimality as the firstbest strategy over all feasible reinsurances is proved. Also, the same optimal reinsurance screening problem is studied under other subclass of reinsurances: (i) deductible contracts; (ii) quotashare reinsurances; and (iii) reinsurance contracts with convex indemnity, with the aid of indirect utility functions. In particular, the optimal indirect utility function is shown to be of the stoploss form under both classes (i) and (ii); while on the other hand, its nonstoploss nature under class (iii) is revealed. Lastly, a class of nonzerosum stochastic differential reinsurance games between two insurance companies is studied. Each insurance company is assumed to maximize the difference of the opponent’s terminal surplus from that of its own by properly arranging its reinsurance schedule. The surplus process of each insurance company is modeled by a mixed regimeswitching CramerLundberg approximation. It is a diffusion risk process with coefficients being modulated by both a continuoustime finitestate Markov Chain and another diffusion process; and correlations among these surplus processes are allowed. In contrast to the traditional HJB approach, BSDE method is used and an explicit Nash equilibrium is derived.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.source.uri  http://hub.hku.hk/bib/B47753031   
dc.subject.lcsh  Reinsurance  Mathematics.   
dc.subject.lcsh  Risk (Insurance)  Mathematics.   
dc.title  Optimal reinsurance: a contemporary perspective   
dc.type  PG_Thesis   
dc.identifier.hkul  b4775303   
dc.description.thesisname  Master of Philosophy   
dc.description.thesislevel  Master   
dc.description.thesisdiscipline  Mathematics   
dc.description.nature  published_or_final_version   
dc.identifier.doi  10.5353/th_b4775303   
dc.date.hkucongregation  2012   