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Mathematical fun with ruin theory
Insurance: Mathematics and Economics, 1988Some classical results of ruin theory are derived by probabilistic methods, which have an interest of their own. Let \(X_ 1\), \(X_ 2\),... be positive, independent and identically distributed random variables with common mean \(\mu\).
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SSRN Electronic Journal, 2016
This paper responds to an ongoing discussion initiated by Duncan Kennedy concerning the identity of "contemporary legal thought." This contribution argues that that category is so hard to define or exemplify because the historical conditions for its possibility are lacking.
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This paper responds to an ongoing discussion initiated by Duncan Kennedy concerning the identity of "contemporary legal thought." This contribution argues that that category is so hard to define or exemplify because the historical conditions for its possibility are lacking.
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Ruin Theory in a Hidden Markov-Modulated Risk Model
Stochastic Models, 2011We discuss ruin theory when the insurance risk process is described by a hidden Markov, regime-switching diffusion process. The innovations approach to filtering theory is used to transform the partially observed modeling framework into one with complete observations. (Robust) filters for the hidden states of the chain are given. A partial differential
Elliott, RJ, Yang, H, Siu, TK
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Ruin theory with compounding assets — a survey
Insurance: Mathematics and Economics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2005
Introduction Ruin theory is concerned with the level of an insurer's surplus for a portfolio of insurance policies. In Chapter 4 we considered the aggregate amount of claims paid out in a single time period. We now consider the evolution of an insurance fund over time, taking account of the times at which claims occur, as well as their amounts.
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Introduction Ruin theory is concerned with the level of an insurer's surplus for a portfolio of insurance policies. In Chapter 4 we considered the aggregate amount of claims paid out in a single time period. We now consider the evolution of an insurance fund over time, taking account of the times at which claims occur, as well as their amounts.
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On Cramér's First Contributions to Ruin Theory
North American Actuarial Journal, 2017In this article, we discuss some of the first contributions due to Harald Cramer to Collective Risk Theory. We examine the introduction and the use of a particular ruin function that nowadays has been lost even if, as we will see, it has many points in common with the severity of ruin.
Ennio Badolati, Sandra Ciccone
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Ruin theory with stochastic return on investments
Advances in Applied Probability, 1997We consider a risk process with stochastic interest rate, and show that the probability of eventual ruin and the Laplace transform of the time of ruin can be found by solving certain boundary value problems involving integro-differential equations. These equations are then solved for a number of special cases.
Paulsen, Jostein, Gjessing, Håkon K.
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Ruin theory in the linear model
Insurance: Mathematics and Economics, 1982Abstract The probability of ruin is examined in a model where the annual gains of an insurance company are dependent random variables. The model used is the linear model (well known in time-series analysis) which includes the autoregressive model and the moving average model as special cases.
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A Gambler's Ruin Type Problem in Queuing Theory
Operations Research, 1963The Takács process, X(t) describing the virtual waiting time or server backlog for a single-server queue with Poisson arrivals and general service time distribution, is discussed with two absorbing boundaries. The process terminates at x = 0 when the server becomes idle or at x = T when a given backlog level is exceeded.
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Ruin Theory Under the Submartingale Assumption
1986The ruin theory is developed under the assumption that the gain process of an insurance company is a submartingale. Gain processes are classified according to the properties of the set of the safety indexes of their increments. Inequalities for ruin probabilities are derived for two important classes of gain processes: the embedable submartingales and ...
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