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Optimizing Insurance and Reinsurance in the Dynamic Cramer–Lundberg Model
Automation and Remote Control. 2012. Vol. 73. No. 9. P. 1529-1538.
A.Yu. Golubin, Gridin V. N.
We find optimal (from the insurer’s point of view) strategies for insurance and reinsurance
in a controllable Cramer–Lundberg risk process that describes the capital dynamics of
an insurance company over an infinite time interval. As the optimality criterion being minimized,
we use the stationary variation coefficient, taking into account additional constraints
on residual risks for both insurers and reinsurer. We establish that it is best to use stop-loss
reinsurance with an upper limit and insurance which is a combination of a stop-loss strategy
and deductible. Equations that define optimal strategies parameters are derived.
Research target:
Mathematics
Language:
English
Golubin A. Y., Gridin V. N., Автоматика и телемеханика 2012 № 9 С. 111-123
В работе найдены оптимальные с точки зрения страховщика стратегии страхования и перестрахования в управляемом процессе риска Крамера-Лундберга, описывающем динамику капитала страховой компании на длительном временном интервале. В качестве минимизируемого критерия оптимальности использовался стационарный коэффициент вариации, были учтены дополнительные ограничения на остаточные риски как страхователей, так и перестраховщика. ...
Added: October 23, 2012
A.Y. Golubin, Scandinavian Actuarial Journal 2016 No. 3 P. 181-197
The paper studies the so-called individual risk model where both a policy of per-claim insurance and a policy of reinsurance are chosen jointly by the insurer in order to maximize his/her expected utility. The insurance and reinsurance premiums are defined by the expected value principle. The problem is solved under additional constraints on the reinsurer's ...
Added: May 6, 2014
Golubin A. Y., Gridin V. N., Газов А. И., Автоматика и телемеханика 2009 Т. 70 № 8 С. 133-144
Статья посвящена решению задач оптимального выбора страховщиком дележей риска клиента на уровне страховщик-клиент и на уровне страховщик-перестраховщик. Показано, что в модели без дополнительных ограничений для страховщика всегда будет наиболее выгодным отказ от перестрахования и применение «stop-loss» стратегии страхования. В задаче, учитывающей ограничение на риск страхователя, лучшим оказывается индивидуальное перестрахование эксцедента убытка («excess of loss») и ...
Added: May 14, 2013
Golubin A. Y., Апарина М. Н., Управление риском 2015 № 1 С. 52-57
The article provides analytical solutions to the following problems: minimization of initial insurer’s capital under
a given ruin probability and maximization of expected utility of the final insurer’s capital. In both cases the insurer can
varies the premium size under a prescribed demand function, that is assumed to be either linear or hyperbolic type.
The results are illustrated ...
Added: April 7, 2015
Golubin A. Y., Gridin V. N., , in : Modern Trends in Controlled Stochastic Processes: Theory and Applications. : Liverpool : Luniver Pre, 2011. P. 216-226.
The chapter studies a dynamic risk model defined on infinite time interval, where both insurance and per-claim reinsurance policies are chosen by the insurer in order to minimize a functional of the form of variation coefficient under constraints imposed with probability one on insured's and reinsurer's risks. We show that the optimum is achieved at ...
Added: April 12, 2012
Golubin A. Y., Automation and Remote Control 2017 Vol. 78 No. 7 P. 1264-1275
In this work, we study the optimal risk sharing problem for an insurer between himself and a reinsurer in a dynamical insurance model known as the Kramer–Lundberg risk process, which, unlike known models, models not per claim reinsurance but rather periodic reinsurance of damages over a given time interval. Here we take into account a ...
Added: October 4, 2017
Саратов : ООО "Издательство "Научная книга", 2016
В сборнике опубликованы материалы V Международной молодежной научно практической конференции «Математическое и компьютерное моделирование в эконо мике, страховании и управлении рисками». Тематика статей затрагивает круг вопросов,
связанных с экономико-математическим и компьютерным моделированием и управле нием рисками в финансовой деятельности, страховании, банковском деле, инвестиро вании, государственном управлении экономикой, бизнес-информатике и других разде лах экономико-математических знаний.
Для сотрудников банков, финансовых и страховых компаний, экономических
отделов ...
Added: February 22, 2017
Golubin A. Y., ASTIN Bulletin 2008 Vol. 38 No. 2 P. 441-460
The concept of economic equilibrium under uncertainty is applied to a model of insurance market where, in distinction to the classic Borch's model of a reinsurance market, risk exchanges are allowed between the insurer and each insured only, not among insureds themselves. Conditions characterizing an equilibrium are found. A variant of the conditions, based on ...
Added: May 14, 2013
Klyukin P. N., Черемных Ю. Н., Saarbrucken : Palmarium Academic Publishing, 2017
Tutorial on mathematical analysis. The manual demonstrates the usefulness of the use of mathematical analysis for a wide range of theoretical and applied economic problems, for example, the task of maximizing the company's profits, the problem of rational consumer behavior in the market, the task of finding a static economic equilibrium. It is of interest ...
Added: October 5, 2018
A.Yu. Golubin, Gridin V. N., Automation and Remote Control 2020 Vol. 81 No. 9 P. 345-357
We investigate a problem of finding an optimal insurance strategy in a multi-stage risk process, where a new type of restrictions for the capital of the insurer is imposed: probabilistic restrictions (Value at Risk constraints) for an increment between the current and next insurer’s capital at the following stage. At each stage, the form of the ...
Added: June 2, 2020
Lazarev A. A., Musatova E. G., Kvaratskhelia A. et al., М. : Физический факультет МГУ, 2012
Данное учебное пособие посвящено задачам теории расписаний, возникающим на транспорте. Представлены основы теории расписаний, а также способы построения моделей и методы решения задач управления транспортными системами. Изложенный материал предназначен для студентов и преподавателей вузов математических специальностей, специалистов в области управления и практиков, занимающихся решением задач планирования грузовых перевозок. ...
Added: December 10, 2012
Golubin A. Y., Gridin V. N., Автоматика и телемеханика 2010 № 8 С. 79-91
The paper studies a problem of optimal insurer’s choice of a risk-sharing policy in a dynamic risk model, so-called Cramer-Lundberg process, over infinite time interval. Additional constraints are imposed on residual risks of insureds: on mean value or with probability one. An optimal control problem of minimizing a functional of the form of variation coefficient ...
Added: April 12, 2012
Lazarev A. A., Kvaratskhelia A., Gafarov E., Доклады Академии наук 2007 Т. 412 № 6 С. 739-742
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Added: November 23, 2012
Кибзун А. И., Panarin S. I., Вестник компьютерных и информационных технологий 2010 № 12 С. 31-40
The stochastic model is provided. Using the model, redesign of distance learning system CLASS.NET is done by solving the stochastic optimization problem. ...
Added: December 5, 2013
Yu. Grishunina, L. Manita, Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 906-909
We propose a new mathematical model of virus spreading over local area networks. We
define a cost functional and consider a maximization problem for the average income given by the
computer network per unit time. ...
Added: September 2, 2017
Golubin A. Y., Гридин В. Н., Автоматика и телемеханика 2020 № 9 С. 144-159
Исследована проблема построения оптимальной стратегии страхования в новой многошаговой модели страхования, где введены пошаговые вероятностные ограничения (Value at Risk (VaR) ограничения) на капитал страховщика, т.е. вероятностные ограничения на приращения капитала страховщика в течение одного шага. В качестве целевого функционала используется математическое ожидание финального капитала страховщика. Суммарный ущерб страховщика на каждом шаге моделируется нормальным распределением с ...
Added: March 10, 2020
Werner F., Lazarev A. A., Automation and Remote Control 2010 Vol. 71 No. 10 P. 2019-2020
Foreword to the thematical issue devoted to the seventieth anniversary of Academician V.S. Tanaev ...
Added: November 23, 2012
Gafarov E., Lazarev A. A., Werner F., Mathematical Social Sciences 2011 No. 62 P. 7-13
We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity ...
Added: November 24, 2012
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 12.
In this paper, we consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. ...
Added: March 4, 2013
A.Y. Golubin, Operations Research Letters 2013 Vol. 41 No. 6 P. 636-638
The paper suggests a new --- to the best of the author's knowledge --- characterization of Pareto-optimal decisions for the case of two-dimensional utility space which is not supposed to be convex. The main idea is to use the angle distances between the bisector of the first quadrant and points of utility space. A necessary ...
Added: October 10, 2013
Gafarov E., Lazarev A. A., Werner F., / Otto-von-Guericke Universitaet. 2010. No. 10.
In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. An NP-hardness proof and a pseudo-polynomial time solution algorithm are proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted ...
Added: March 4, 2013
Lazarev A. A., Kvaratskhelia A., Автоматика и телемеханика 2010 № 10 С. 80-89
In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases. ...
Added: November 24, 2012
Gafarov E., Lazarev A. A., Werner F., Annals of Operations Research 2012 Vol. 196 No. 1 P. 247-261
We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed.We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity ...
Added: November 24, 2012
Lazarev A. A., Gafarov E., Доклады Академии наук 2008 Т. 424 № 1 С. 7-9
27.47.19 Исследование операций
28.15.19 Нелинейные детерминированные системы
28.19.15 Оптимальные системы
28.29.15 Методы исследования операций ...
Added: November 23, 2012