Academic literature on the topic 'Ntegral equation for the non - ruin probability'
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Journal articles on the topic "Ntegral equation for the non - ruin probability"
Guilbault, Jean-Luc, and Mario Lefebvre. "On a non-homogeneous difference equation from probability theory." Tatra Mountains Mathematical Publications 43, no. 1 (December 1, 2009): 81–90. http://dx.doi.org/10.2478/v10127-009-0027-4.
Full textQuang, Phung Duy. "Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains." East Asian Journal on Applied Mathematics 4, no. 3 (August 2014): 283–300. http://dx.doi.org/10.4208/eajam.051013.230614a.
Full textMøller, Christian Max. "Stochastic differential equations for ruin probabilities." Journal of Applied Probability 32, no. 01 (March 1995): 74–89. http://dx.doi.org/10.1017/s002190020010258x.
Full textMøller, Christian Max. "Stochastic differential equations for ruin probabilities." Journal of Applied Probability 32, no. 1 (March 1995): 74–89. http://dx.doi.org/10.2307/3214922.
Full textAsmussen, Søren, and Hanne Mandrup Nielsen. "Ruin probabilities via local adjustment coefficients." Journal of Applied Probability 32, no. 3 (September 1995): 736–55. http://dx.doi.org/10.2307/3215126.
Full textAsmussen, Søren, and Hanne Mandrup Nielsen. "Ruin probabilities via local adjustment coefficients." Journal of Applied Probability 32, no. 03 (September 1995): 736–55. http://dx.doi.org/10.1017/s0021900200103171.
Full textBondarev, B. V., and V. O. Boldyreva. "Deriving the Equation for the Non-Ruin Probability of the Insurance Company in (B, S)-market. Stochastic Claims and Stochastic Premiums." Cybernetics and Systems Analysis 50, no. 5 (September 2014): 750–58. http://dx.doi.org/10.1007/s10559-014-9665-x.
Full textAssaf, David, Yuliy Baryshnikov, and Wolfgang Stadje. "Optimal strategies in a risk selection investment model." Advances in Applied Probability 32, no. 02 (June 2000): 518–39. http://dx.doi.org/10.1017/s0001867800010065.
Full textAssaf, David, Yuliy Baryshnikov, and Wolfgang Stadje. "Optimal strategies in a risk selection investment model." Advances in Applied Probability 32, no. 2 (June 2000): 518–39. http://dx.doi.org/10.1239/aap/1013540177.
Full textDissertations / Theses on the topic "Ntegral equation for the non - ruin probability"
Федчишина, Ірина Юріївна. "Уточнення апроксимації де Вілдера для оцінки ймовірності банкрутства у страховій моделі Крамера-Лундберга." Master's thesis, Київ, 2018. https://ela.kpi.ua/handle/123456789/23449.
Full textIn the master's thesis a new approach to the approximate finding of the ruin probability of an insurance company on an infinite time horizon is proposed. The need for such an approximate finding is due to the fact that the exact value of the ruin probability, being a solution to a complex integral equation, can often not be expressed in explicit analytical form. The idea of the developed method is to replace the process of risk with another risk process with insurance payments distributed according to the law, which is a mixture of two exponential distributions. For such a risk process, the ruin probability is known in analytical form. Replacement is realized by equating the first five cumulants of the initial and new risk processes.
В магистерской диссертации предложен новый поход к приближенному нахождению вероятности банкротства страховой компании на бесконечном временном горизонте. Необходимость такого приближенного нахождения обусловлено тем, что точное значение вероятности банкротства, будучи решением сложного интегрального уравнения, часто не может быть выражено в явной аналитической форме. Идея разработанного метода заключается в замене процесса страхового риска на другой процесс риска со страховыми выплатами, распределенными по закону, который является смесью двух экспоненциальных распределений. Для такого процесса риска вероятность банкротства известна в аналитической форме. Замена реализуется путем приравнивания первых пяти кумулянтов начального и нового процессов риска.
Ni, Ying. "Perturbed Renewal Equations with Non-Polynomial Perturbations." Licentiate thesis, Mälardalen University, School of Education, Culture and Communication, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-9354.
Full textThis thesis deals with a model of nonlinearly perturbed continuous-time renewal equation with nonpolynomial perturbations. The characteristics, namely the defect and moments, of the distribution function generating the renewal equation are assumed to have expansions with respect to a non-polynomial asymptotic scale: $\{\varphi_{\nn} (\varepsilon) =\varepsilon^{\nn \cdot \w}, \nn \in \mathbf{N}_0^k\}$ as $\varepsilon \to 0$, where $\mathbf{N}_0$ is the set of non-negative integers, $\mathbf{N}_0^k \equiv \mathbf{N}_0 \times \cdots \times \mathbf{N}_0, 1\leq k <\infty$ with the product being taken $k$ times and $\w$ is a $k$ dimensional parameter vector that satisfies certain properties. For the one-dimensional case, i.e., $k=1$, this model reduces to the model of nonlinearly perturbed renewal equation with polynomial perturbations which is well studied in the literature. The goal of the present study is to obtain the exponential asymptotics for the solution to the perturbed renewal equation in the form of exponential asymptotic expansions and present possible applications.
The thesis is based on three papers which study successively the model stated above. Paper A investigates the two-dimensional case, i.e. where $k=2$. The corresponding asymptotic exponential expansion for the solution to the perturbed renewal equation is given. The asymptotic results are applied to an example of the perturbed risk process, which leads to diffusion approximation type asymptotics for the ruin probability. Numerical experimental studies on this example of perturbed risk process are conducted in paper B, where Monte Carlo simulation are used to study the accuracy and properties of the asymptotic formulas. Paper C presents the asymptotic results for the more general case where the dimension $k$ satisfies $1\leq k <\infty$, which are applied to the asymptotic analysis of the ruin probability in an example of perturbed risk processes with this general type of non-polynomial perturbations. All the proofs of the theorems stated in paper C are collected in its supplement: paper D.