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) Zoneadaptive
control strategy for a multiperiodic model of risk. Contribution
to: 38th ASTIN Colloquium (July 1316, 2008, Manchester, UK).
Abstract:
In this paper intended to illustrate the adaptive control
approach in insurance, a zoneadaptive
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
Poissonexponential multiperiodic risk
model. The room for further generalizations is large. In
particular, it is the risk theory insight into the
problem of assetliability 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.
Abstract
Paper
Presentation
Malinovskii, V.K. (2008) Risk theory
insight into a zoneadaptive control strategy.
Insurance: Mathematics and Economics, 42, 656667.
Abstract:
The main purpose of the paper is a risk theory insight into the
problem of assetliability and
solvency adaptive management. In the multiperiodic
insurance risk model composed of chained classical risk
models, a zoneadaptive
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, 8194.] 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.
Title page of the paper
References
References
Malinovskii, V.K. (2008) Adaptive
control strategies and dependence of finite time ruin on the
premium loading. Insurance: Mathematics and Economics, 42,
8194.
Abstract:
The paper is devoted to risk theory insight into the problem of
assetliability 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
References
Malinovskii, V.K. (2006) Risk theory
insight into the assetliability 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
assetliability balance in the multiperiod controlled
risk model composed of chained singleperiodic
PoissonExponential 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 nonlinear
dynamic solvency control model. Contribution to:
34th ASTIN
Colloquium (August 2427, 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 1722, 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 goingconcern philosophy).
Paper
Malinovskii, V.K. (2000) Price vs.
reserve regulation conditioned by solvency requirements in the
collective risk model. Contribution to:
31st International ASTIN
Colloquium (1720.09.2000, 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, 885923.
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
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 (712.6.1998, 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) NonPoissonian
claims arrivals and calculation of the probability of ruin,
Insurance: Mathematics and Economics, vol. 22, 123138.
Abstract:
Collective risk model with a special emphasize on nonPoissonian
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 nonPoissonian 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, 124147.
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 $0<t(u)\ll {\mu_T}{\mu_X}^{1} u$, as
the initial risk reserve $u$ increases
to infinity, are suggested. This result complements the
classical normaltype approximation
for the probability of ruin within finite
time and is designed as its large deviations counterpart.
The main technical device of the paper
(see Section 3), which is of independent interest, are the
upper bounds and the asymptotic
expressions for the probabilities of large
deviations of the stopped random walks, developed under
low moment conditions.
Title page of the paper
References
Malinovskii, V.K. (1994) Corrected normal
approximation for the probability of ruin within finite time,
Scandinavian Actuarial Journal, 161174.
Abstract:
A new secondorder approximation for the probability of ruin
before time $t$ in the framework of
Andersen's risk model is suggested.
This approximation is proved to be a
refinement of the classical normaltype approximation and
is deduced from von Bahr's
representation of ruin probability in terms of ladder
height distributions. The proof is
based on the use of technique developed in
Malinovskii (1993) and designed for the analysis of
stopped random sequences
which allow the embedding of a blockwise structure.
Title page of the paper
References
References
