Related papers: Discrete time risk models with m-dependent random …
We consider the multivariate risk model with common renewal process among the lines of business, and Brownian perturbations. Assuming that the integrated tail distribution of claims is multivariate subexponential, we establish an asymptotic…
Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics.…
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…
Interval-censored competing risks data arise when each study subject may experience an event or failure from one of several causes and the failure time is not observed exactly but rather known to lie in an interval between two successive…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance…
Assessing the causal effect of time-varying exposures on recurrent event processes is challenging in the presence of a terminating event. Our objective is to estimate both the short-term and delayed marginal causal effects of exposures on…
The generalization performance of a risk prediction model can be evaluated by its calibration, which measures the agreement between predicted and observed outcomes on external validation data. Here, methods for assessing the calibration of…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
In this paper, we study finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…
The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We…
In this paper, we study a dual risk model with delays in the spirit of Dassios-Zhao. When a new innovation occurs, there is a delay before the innovation turns into a profit. We obtain large initial surplus asymptotics for the ruin…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…
We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics,…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…