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We revisit the famous Mack's model which gives an estimate for the conditional mean squared error of prediction of the chain-ladder claims reserves. We introduce a stochastic differential equation driven by a Brownian motion to model the…
In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…
The appropriate estimation of incurred but not reported (IBNR) reserves is traditionally one of the most important task of actuaries working in casualty and property insurance. As certain claims are reported many years after their…
Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic…
Incurred but not reported (IBNR) loss reserving is an important issue for Property & Casualty (P&C) insurers. The modeling of the claim arrival process, especially its temporal dependence, has not been closely examined in many of the…
The paper proposes an original methodology for constructing quantitative statistical models based on multidimensional distribution functions constructed on the basis of the insurance companies' data on inshurance policies (including…
Claims reserving, also known as Incurred But Not Reported (IBNR) claims prediction, is an important issue in general insurance. State space modeling is widely recognized as a statistically robust method for addressing this problem. In state…
There are growing concerns for reserves estimation of incurred but not reported (IBNR) claims in actuarial sciences. In this paper, we propose a copula-based dependency model to capture the relationship between two main IBNR reserve…
The reporting delay in data breach incidents poses a formidable challenge for Incurred But Not Reported (IBNR) studies, complicating reserve estimation for actuarial professionals. This work presents a novel Bayesian nowcasting model…
Within the Solvency II framework the insurance industry requires a realistic modelling of the risk processes relevant for its business. Every insurance company should be capable of running a holistic risk management process to meet this…
The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…
In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated…
This paper introduces a unified micro-level stochastic framework for the joint modeling of loss reserves (RBNS), incurred but not reported (IBNR) reserves, and unearned premium risk under dependence, inflation, and discounting. The proposed…
We propose a coupled bootstrap (CB) method for the test error of an arbitrary algorithm that estimates the mean in a Poisson sequence, often called the Poisson means problem. The idea behind our method is to generate two carefully-designed…
Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…
Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution…
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…
This paper presents a multinomial multi-state micro-level reserving model, denoted mCube. We propose a unified framework for modelling the time and the payment process for IBNR and RBNS claims and for modeling IBNR claim counts. We use…
For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…