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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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Inequality extensions of Prabhu’s formula in ruin theory
Insurance: Mathematics and Economics, 1999Abstract Prabhu’s formula in the classical actuarial risk model expresses the non-ruin probability in the bounded time interval [0, t ] as a function of the distribution of the total claim amount in that interval. It is valid in case of an initial risk reserve u =0 only.
F.E.C. De Vylder +2 more
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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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2005
Introduction In this chapter we continue our study of the classical risk model. We start with a useful result concerning the probability that ruin occurs without the surplus process first attaining a specified level. This result will be applied in Sections 8.4 and 8.5 and Exercise 9. We then consider the insurer's deficit when ruin occurs and provide
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Introduction In this chapter we continue our study of the classical risk model. We start with a useful result concerning the probability that ruin occurs without the surplus process first attaining a specified level. This result will be applied in Sections 8.4 and 8.5 and Exercise 9. We then consider the insurer's deficit when ruin occurs and provide
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2016
Classical ruin theory was developed by Lundberg in 1907 and refined by Cramer in 1930. This theory describes the evolution of the surplus of an insurance company over time. It assumes that an insurance company begins with an initial surplus and then receives premiums continuously at a constant rate. It also assumes that claims of random and independent
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Classical ruin theory was developed by Lundberg in 1907 and refined by Cramer in 1930. This theory describes the evolution of the surplus of an insurance company over time. It assumes that an insurance company begins with an initial surplus and then receives premiums continuously at a constant rate. It also assumes that claims of random and independent
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Growth paths and survival chances: An application of Gambler's Ruin theory [PDF]
Journal of Business Venturing, 2013 This paper links new firm survival with growth, with a focus on the patterns in firms' growth paths. We theorise a Gambler's Ruin framework by arguing that new firm performance is best modelled as a random walk process, but that survival is nonrandom and depends primarily on the stock of accumulated resources.
David Storey +5 more
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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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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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Ruin Theory for the Risk Process Described by PDMPs
Acta Mathematicae Applicatae Sinica, English Series, 2003In this paper we consider the risk process that is described by a piecewise deterministic Markov processes (PDMP). We first present the construction of the risk process and then discuss some ruin problems for this new kind of risk model.
Rong Wu, Guo-jing Wang, Chun-sheng Zhang
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A podcast on urban ruins, or the aural weaving of theory and field
cultural geographies, 2019Making a podcast can be a way to weave together concepts, theories or mere thoughts about places, and the aural sensory experience of being in place. In this short article, we present the NoVOID podcast, an audio podcast on ruins and vacant lands that combines interviews with scholars from various fields of knowledge and field recordings in various ...
Paiva, Daniel, Brito-Henriques, Eduardo
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