Graphical Models for Groups: Belief Aggregation and Risk Sharing

2005 ◽  
Vol 2 (3) ◽  
pp. 148-164 ◽  
Author(s):  
David M. Pennock ◽  
Michael P. Wellman
2021 ◽  
pp. 1-27
Author(s):  
Michel Denuit ◽  
Christian Y. Robert

Abstract Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.


Author(s):  
Truman Packard ◽  
Ugo Gentilini ◽  
Margaret Grosh ◽  
Philip O’Keefe ◽  
Robert Palacios ◽  
...  
Keyword(s):  

Author(s):  
Mauricio Drelichman ◽  
Hans-Joachim Voth

Why do lenders time and again loan money to sovereign borrowers who promptly go bankrupt? When can this type of lending work? As the United States and many European nations struggle with mountains of debt, historical precedents can offer valuable insights. This book looks at one famous case—the debts and defaults of Philip II of Spain. Ruling over one of the largest and most powerful empires in history, King Philip defaulted four times. Yet he never lost access to capital markets and could borrow again within a year or two of each default. Exploring the shrewd reasoning of the lenders who continued to offer money, the book analyzes the lessons from this historical example. Using detailed new evidence collected from sixteenth-century archives, the book examines the incentives and returns of lenders. It provides powerful evidence that in the right situations, lenders not only survive despite defaults—they thrive. It also demonstrates that debt markets cope well, despite massive fluctuations in expenditure and revenue, when lending functions like insurance. The book unearths unique sixteenth-century loan contracts that offered highly effective risk sharing between the king and his lenders, with payment obligations reduced in bad times. A fascinating story of finance and empire, this book offers an intelligent model for keeping economies safe in times of sovereign debt crises and defaults.


2019 ◽  
Author(s):  
Julian Burger ◽  
Margaret S. Stroebe ◽  
Pasqualina Perrig-Chiello ◽  
Henk A.W. Schut ◽  
Stefanie Spahni ◽  
...  

Background: Prior network analyses demonstrated that the death of a loved one potentially precedes specific depression symptoms, primarily loneliness, which in turn links to other depressive symptoms. In this study, we extend prior research by comparing depression symptom network structures following two types of marital disruption: bereavement versus separation. Methods: We fitted two Gaussian Graphical Models to cross-sectional data from a Swiss survey of older persons (145 bereaved, 217 separated, and 362 married controls), and compared symptom levels across bereaved and separated individuals. Results: Separated compared to widowed individuals were more likely to perceive an unfriendly environment and oneself as a failure. Both types of marital disruption were linked primarily to loneliness, from where different relations emerged to other depressive symptoms. Amongst others, loneliness had a stronger connection to perceiving oneself as a failure in separated compared to widowed individuals. Conversely, loneliness had a stronger connection to getting going in widowed individuals. Limitations: Analyses are based on cross-sectional between-subjects data, and conclusions regarding dynamic processes on the within-subjects level remain putative. Further, some of the estimated parameters in the network exhibited overlapping confidence intervals and their order needs to be interpreted with care. Replications should thus aim for studies with multiple time points and larger samples. Conclusions: The findings of this study add to a growing body of literature indicating that depressive symptom patterns depend on contextual factors. If replicated on the within-subjects level, such findings have implications for setting up patient-tailored treatment approaches in dependence of contextual factors.


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