182 research outputs found
The Finite-time Ruin Probabilities of a Bidimensional risk model with Constant Interest Force and correlated Brownian Motions
We follow some recent works to study bidimensional perturbed compound Poisson
risk models with constant interest force and correlated Brownian Motions.
Several asymptotic formulae for three different type of ruin probabilities over
a finite-time horizon are established.
Our approach appeals directly to very recent developments in the ruin theory
in the presence of heavy tails of unidimensional risk models and the dependence
theory of stochastic processes and random vectors.Comment: 25page
Finite-time ruin probability of a perturbed risk model with dependent main and delayed claims
This paper considers a delayed claim risk model with stochastic return and Brownian perturbation in which each main claim may be accompanied with a delayed claim occurring after a stochastic period of time, and the price process of the investment portfolio is described as a geometric Lévy process. By means of the asymptotic results for randomly weighted sum of dependent subexponential random variables we obtain some asymptotics for finite-time ruin probability. A simulation study is also performed to check the accuracy of the obtained theoretical result via the crude Monte Carlo method
Interplay of insurance and financial risks in a discrete-time model with strongly regular variation
Consider an insurance company exposed to a stochastic economic environment
that contains two kinds of risk. The first kind is the insurance risk caused by
traditional insurance claims, and the second kind is the financial risk
resulting from investments. Its wealth process is described in a standard
discrete-time model in which, during each period, the insurance risk is
quantified as a real-valued random variable equal to the total amount of
claims less premiums, and the financial risk as a positive random variable
equal to the reciprocal of the stochastic accumulation factor. This risk model
builds an efficient platform for investigating the interplay of the two kinds
of risk. We focus on the ruin probability and the tail probability of the
aggregate risk amount. Assuming that every convex combination of the
distributions of and is of strongly regular variation, we derive some
precise asymptotic formulas for these probabilities with both finite and
infinite time horizons, all in the form of linear combinations of the tail
probabilities of and . Our treatment is unified in the sense that no
dominating relationship between and is required.Comment: Published at http://dx.doi.org/10.3150/14-BEJ625 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
At the Edge of Criticality: Markov Chains with Asymptotically Zero Drift
In Chapter 2 we introduce a classification of Markov chains with
asymptotically zero drift, which relies on relations between first and second
moments of jumps. We construct an abstract Lyapunov functions which looks
similar to functions which characterise the behaviour of diffusions with
similar drift and diffusion coefficient.
Chapter 3 is devoted to the limiting behaviour of transient chains. Here we
prove converges to and normal distribution which generalises papers by
Lamperti, Kersting and Klebaner. We also determine the asymptotic behaviour of
the cumulative renewal function.
In Chapter 4 we introduce a general strategy of change of measure for Markov
chains with asymptotically zero drift. This is the most important ingredient in
our approach to recurrent chains.
Chapter 5 is devoted to the study of the limiting behaviour of recurrent
chains with the drift proportional to . We derive asymptotics for a
stationary measure and determine the tail behaviour of recurrence times. All
these asymptotics are of power type.
In Chapter 6 we show that if the drift is of order then moments
of all orders are important for the behaviour of stationary
distributions and pre-limiting tails. Here we obtain Weibull-like asymptotics.
In Chapter 7 we apply our results to different processes, e.g. critical and
near-critical branching processes, risk processes with reserve-dependent
premium rate, random walks conditioned to stay positive and reflected random
walks.
In Chapter 8 we consider asymptotically homogeneous in space Markov chains
for which we derive exponential tail asymptotics
Heavy-tailed distribution in the presence of dependence in insurance and finance
In the past decade, the study of the renewal risk model in the presence of dependent insurance and financial risks and heavy-tailed claims is one of the key topics in modern risk theory. The purpose of this thesis is to study the renewal risk model with certain dependence structures. We also assume that claim sizes follow a heavy-tailed distribution, in particular, a subexponential distribution. We focus on studying the impact of heavy tails and dependence structures on ruin probabilities and the tail probabilities of aggregate claims. For the study of dependence structure, we consider two assumptions here, namely, dependence between claims and inter-arrival times and dependence between insurance and financial risks, particular attention are paid for the dependent insurance and financial risks. In this case, an equation for the tail probability of maximal present value of aggregate net loss is derived, and hence some insights into the ruin probability can be obtained
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