Professional Links Professional Journals Forthcoming Events

RESEARCH ARTICLES

 V.K. Malinovskii is the author of more than 50 research papers in diverse fields of Theory of Probability, Statistics and Random Processes. Among his papers in Risk Theory are:   Malinovskii, V.K. (2008) Zone-adaptive control strategy for a multiperiodic model of risk. Contribution to: 38th ASTIN Colloquium (July 13-16, 2008, Manchester, UK).   Abstract: In this paper intended to illustrate the adaptive control approach in insurance, a zone-adaptive control strategy harmonizing the requirements of principles of solvency and equity is considered in the simplistic framework of diffusion multiperiodic risk model. The adjacent works by the author set the similar adaptive control strategies in more realistic Poisson-exponential multiperiodic risk model. The room for further generalizations is large. In particular, it is the risk theory insight into the problem of asset-liability and solvency adaptive management in insurance under deficient information. The latter means that the intensities of the successive annual claim arrival processes are the random variables which comply with a certain scenario.       Malinovskii, V.K. (2008) Risk theory insight into a zone-adaptive control strategy. Insurance: Mathematics and Economics, 42, 656-667.   Abstract: The main purpose of the paper is a risk theory insight into the problem of asset-liability and solvency adaptive management. In the multiperiodic insurance risk model composed of chained classical risk models, a zone-adaptive control strategy, essentially similar to that applied in Directives [Directive 2002/13/EC of the European Parliament and of the Council of 5 March 2002, Brussels, 5 March 2002], is introduced and its performance is examined analytically. That examination was initiated in [Malinovskii, V.K., 2006b. Adaptive control strategies and dependence of finite time ruin on the premium loading. Insurance: Math. Econ., 42, 81-94.] and is based on the application of the explicit expression for the finite time ruin probability in the classical risk model. The result of independent interest in the paper is the representation of that finite time ruin probability in terms of asymptotic series, as time increases.       Malinovskii, V.K. (2008) Adaptive control strategies and dependence of finite time ruin on the premium loading. Insurance: Mathematics and Economics, 42, 81-94.   Abstract: The paper is devoted to risk theory insight into the problem of asset-liability and solvency adaptive management. Two adaptive control strategies in the multiperiodic insurance risk model composed of chained classical risk models are introduced and their performance in terms of probability of ruin is examined. The analysis is based on an explicit expression of the probability of ruin within finite time in terms of Bessel functions. Dependence of that probability on the premium loading, either positive or negative, is basic technical result of independent interest. Title page of the paper References     Malinovskii, V.K. (2006) Risk theory insight into the asset-liability and solvency adaptive management. Contribution to: 28th International Congress of Actuaries, Paris, May, 2006. Abstract: Bearing in mind the problem of underwriting cycles, two adaptive control strategies regulating the asset-liability balance in the multiperiod controlled risk model composed of chained singleperiodic Poisson-Exponential risk models, are introduced. Solvency performance of these strategies in terms of the probabilities of ruin is analyzed analytically. The strategies are similar, but less sophisticated, than the existent compulsory regulatory procedures. Paper     Malinovskii, V.K. (2003) On a non-linear dynamic solvency control model. Contribution to: 34th ASTIN Colloquium (August 24-27, 2003, Berlin, Germany). Abstract: A dynamic control model of the insurance process over $n$ successive accounting years is considered. The analytical inference about the model requires investigations of a class of kernels describing yearly insurance mechanism. Aiming the kernels, the approximations for the distribution of the risk reserve at time $t$ conditional on ruin within time $t$ in the Andersen's collective risk model are obtained. Corrected approximations for the mean and certain numerical results are also presented.. Paper     Malinovskii V.K. (2002) On risk reserve conditioned by ruin. Contribution to: 27th International Congress of Actuaries (March 17--22, 2002, Cancun, Mexico). Abstract: The distribution of the risk reserve at time $t$ conditional on ruin within time $t$ is considered in Andersen's collective risk model. Approximations for large initial capital and certain numerical results are presented. The problem is motivated by the wish to get more insight on the consequences of ruin during the time interval $(0,t]$. In particular, what would be the capital of a company at the end of the accounting period if, once ruin has occurred, the insurer's usual activities continued during this period, including the acceptance of new business (a sort of going-concern philosophy).        Malinovskii, V.K. (2000) Price vs. reserve regulation conditioned by solvency requirements in the collective risk model. Contribution to: 31st International ASTIN Colloquium (17--20.09.2000, Porto Cervo, Italy). Abstract: The policy prices adjusted vs. reserves conditioned by solvency in a short term time horizon are considered. The motivation is to step towards considering insurer as subject of price competitive insurance market. The intrinsic relationship between policy prices and reserves and its influence on solvency of individual insurance business are formalized in the framework of the collective risk model. Different approaches to tuning prices vs. reserves conditioned by solvency requirements expressed in terms of the probability of ruin within finite time and of the ultimate ruin probability, based on (a) exact numerical technique, (b) new approximations, and (c) simulation, are discussed. Paper     Malinovskii, V.K. (2000) Probabilities of ruin when the safety loading tends to zero, Advances in Applied Probability, vol. 32, 885-923. Abstract: When the premium rate is a positive absolute constant throughout the time period of observation and the safety loading of the insurance business is positive, a classical result of collective risk theory claims that probabilities of ultimate ruin $\psi (u)$ and of ruin within finite time $\psi (t,u)$ decrease as $e^{-\varkappa u}$ with a constant $\varkappa>0$, as the initial risk reserve $u$ increases. This paper establishes uniform approximations to $\psi (t,u)$ with slower rates of decrease when the premium rate depends on $u$ in such a way that the safety loading decreases to zero as $u\to\infty$. Title page of the paper References     Malinovskii, V.K. (1998) Some aspects of rate making and collective risk models with variable safety loadings. Contribution to: 26th International Congress of Actuaries (7--12.6.1998, Birmingham, UK). Abstract: The problem of rate making and solvency analysis is considered. A modification of the collective risk model that amounts to eventual decreasing of the premium rates, as the initial risk reserve grows, is introduced. Being of greater complexity, this model could better reflect some important aspects of real life, in particular in what concerns competitive insurance markets and comprehensive insurance, and has methodological advances. The rates of decreasing of the corresponding probabilities of ruin are different from the classical Cramérian exponent. Though only the case of light tailed distributions is considered, a great diversity of the rates including in particular power ones, emerges. The power rates appeared previously only in the context of heavy tailed claim amounts distributions. Paper     Malinovskii, V.K. (1998) Non-Poissonian claims arrivals and calculation of the probability of ruin, Insurance: Mathematics and Economics, vol. 22, 123-138. Abstract: Collective risk model with a special emphasize on non-Poissonian claims arrival processes is considered. Exact and approximate techniques for calculation of the probabilities of ruin are examined. Simulation going back to the importance sampling is applied to two particular cases of non-Poissonian claims arrival processes to illustrate strong dependence of the probabilities of ruin on the interclaims distribution. Title page of the paper References     Malinovskii, V.K. (1996) Approximations and upper bounds on probabilities of large deviations in the problem of ruin within finite time, Scandinavian Actuarial Journal, 124-147. Abstract: In the framework of Andersen's risk model, a new asymptotic expression and upper bounds on probabilities of ruin after time $t(u)\gg {\mu_T} {\mu_X}^{-1} u$ and before time \$0