臺灣博碩士論文加值系統

本文旨在討論風險資產及破產機率之相關問題。於短期風險模型方面，文中提供
數個範例，並運用機率論定理以利計算；至於長期風險模型，則探討Cramér-Lundberg
Model，且聚焦於破產機率與破產時損失之分佈函數，採取兩種方法計算前者。最後介
紹合計損失的概念，透過對合計損失的分析，得以獲取若干關於風險資產的新觀點。

The main objects of our study is to consider the risk processes in insurance and to
discuss their ruin probability. When it comes to the short term risk model, we show some
examples and briefly discuss how the theorems from probability theory can be used to
perform analysis. For the long term risk model, we discuss the Cramér-Lundberg Model,
in which we are interested in the ruin probability and the distribution of the loss when a
ruin occurs. Two methods are given to calculate the ruin probability. Also, we introduce
the idea of aggregate loss for the study of risk process, which can be used to do the
analysis from another point of view. In the first two sections, we briefly discuss the utility
function and give a review of the basic probability theory.

摘要 i
Abstract ii
Contents iii
Chapter 1 Introduction 1
Chapter 2 Utility theory and insurance 3
Chapter 3 Basic tools from probability theory 9
Chapter 4 The individual risk model and collective risk models 15
Chapter 5 Ruin theory 23
References 45

[1] Rob Kaas, Marc Goovaerts, Jan Dhaene and Michel Denuit (2001) ''Modern Actuarial Risk Theory.'' Kluwer Academic Publishers.
[2] Jan Grandell (1991) ''Aspects of Risk Theory.'' Springer-Verlag.
[3] Hun Seog (2010) ''The economics of Risk and Insurance.'' Wiley-Blackwell.
[4] George Casella and Roger L.Berger (2002) ''Statistical Inference, Second Edition.'' Brooks/Cole, Cengage Learning.
[5] Sidney I. Resnick (2003) ''A Probability Path.'' Birkhäuser Boston.