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Ruin Probability Functions and Severity of Ruin as a Statistical Decision Problem [PDF]
Risks, 2019 It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus,
Emilio Gómez-Déniz +2 more
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Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables [PDF]
Entropy, 2023 In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive ...
Lihong Guan, Xiaohong Wang
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On the expected discounted penalty function at ruin of a surplus process with interest [PDF]
Insurance: Mathematics and Economics, 2002 The paper deals with the ruin problem for an insurer, who receives interest on its surplus at time \(t\), \(U_{\delta}(t)\), at the constant force \(\delta\) per unit time. In particular the expected value of a discounted penalty function at ruin is investigated. Denoted by \(T_{\delta}\) the time of ruin, \(u\) the inizial surplus and \(\alpha\) a non-
David Dickson, Jun Cai
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Analyzing Sequential Betting with a Kelly-Inspired Convective-Diffusion Equation [PDF]
EntropyThe purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and
Darrell Velegol, Kyle J. M. Bishop
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A note on some joint distribution functions involving the time of ruin [PDF]
Insurance: Mathematics and Economics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Dickson
exaly +4 more sources
Ruin probabilities and penalty functions with stochastic rates of interest
Stochastic Processes and Their Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Cai
exaly +3 more sources
Journal of Mathematics, 2022 In this paper, the intention was to reduce the possibility of ruin in the insurance company by maximizing its survival function. This paper uses a perturbed classical risk process as the basic model.
Masoud Komunte +2 more
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International Journal of Mathematics for Industry, 2023 This paper studies the Gerber–Shiu function for the insurance surplus process with additional investment under the Bachelier model. The Gerber–Shiu function allows us to study the moments of the time of ruin, which is the first time that the surplus is ...
Sutipon Punaluek, Yuri Imamura
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Ruin probabilities as functions of the roots of a polynomial
Modern Stochastics: Theory and Applications, 2023 A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided when the claims are assumed to follow a finite mixture of m Erlang distributions. Using the theory of recurrence sequences, the method proposed here shifts the problem of finding the ruin probability to the study of an associated characteristic polynomial ...
David J. Santana, Luis Rincón
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On a Fractional Stochastic Risk Model with a Random Initial Surplus and a Multi-Layer Strategy
Mathematics, 2022 The paper deals with a fractional time-changed stochastic risk model, including stochastic premiums, dividends and also a stochastic initial surplus as a capital derived from a previous investment.
Enrica Pirozzi
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