Applying State Space Models to Stochastic Claims Reserving

Abstract

The paper solves the loss reserving problem using Kalman recursions in linear statespace models. In particular, if one orders claims data from run-off triangles to time series with missing observations, then state space formulation can be applied for projections or interpolations of IBNR (Incurred But Not Reported) reserves. Namely, outputs of the corresponding Kalman recursion algorithms for missing or future observations can be taken as the IBNR projections. In particular, by means of such recursive procedures one can perform effectively simulations in order to estimate numerically the distribution of IBNR claims which may be very useful in terms of setting and/or monitoring of prudency level of loss reserves. Moreover, one can generalize this approach to the multivariate case of several dependent run-off triangles for correlated business lines and the outliers in claims data can be also treated effectively in this way. Results of a numerical study for several sets of claims data (univariate and multivariate ones) are presented.

Stochastic Claims Reserving Methods with State Space Representations: A Review

“…Chukhrova and Johannssen (2017) presented a scalar state space model for cumulative payments. Most recently, Costa and Pizzinga (2020) and Hendrych and Cipra (2021) extended the row-wise stacking approach from Atherino et al (2010) through the inclusion of tail effects and multivariate considerations that allow for dependency modeling between correlated lines of business, respectively.…”

Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving

“…Recently, some articles have been published that deal with SSMs in stochastic claims reserving (see Avanzi et al 2020;Costa and Pizzinga 2020;Hendrych and Cipra 2021). The main aspects involved are multivariate SSMs, which allow for the incorporation of claims activity dynamics and modeling of dependencies between correlated lines of business (Avanzi et al 2020;Hendrych and Cipra 2021), as well as the concept of rowwise stacking the claims development data within run-off triangles to form a univariate time series (Costa and Pizzinga 2020;Hendrych and Cipra 2021).…”

“…Recently, some articles have been published that deal with SSMs in stochastic claims reserving (see Avanzi et al 2020;Costa and Pizzinga 2020;Hendrych and Cipra 2021). The main aspects involved are multivariate SSMs, which allow for the incorporation of claims activity dynamics and modeling of dependencies between correlated lines of business (Avanzi et al 2020;Hendrych and Cipra 2021), as well as the concept of rowwise stacking the claims development data within run-off triangles to form a univariate time series (Costa and Pizzinga 2020;Hendrych and Cipra 2021). Moreover, the authors address issues such as calendar year reserve prediction, inclusion of tail effects (Costa and Pizzinga 2020), a two-dimensional evolution of factors across accident and calendar years (Avanzi et al 2020), and a unified modeling of various common approaches (log-normal models, Hoerl curve approaches etc) within the same kind of state space representation (Hendrych and Cipra 2021).…”

“…The main aspects involved are multivariate SSMs, which allow for the incorporation of claims activity dynamics and modeling of dependencies between correlated lines of business (Avanzi et al 2020;Hendrych and Cipra 2021), as well as the concept of rowwise stacking the claims development data within run-off triangles to form a univariate time series (Costa and Pizzinga 2020;Hendrych and Cipra 2021). Moreover, the authors address issues such as calendar year reserve prediction, inclusion of tail effects (Costa and Pizzinga 2020), a two-dimensional evolution of factors across accident and calendar years (Avanzi et al 2020), and a unified modeling of various common approaches (log-normal models, Hoerl curve approaches etc) within the same kind of state space representation (Hendrych and Cipra 2021). Especially in the today's data-driven insurance business, the handling of Big Data and of dependencies across a huge number of multiple business segments (business lines and their various subsets) are crucial characteristics of claims reserving for insurance companies.…”

“…Alongside the row-wise stacking approach (see Atherino et al 2010;Costa and Pizzinga 2020;Hendrych and Cipra 2021) there are some other approaches to construct state space models in stochastic claims reserving. The most prevalent approach is a calendar-yearbased modeling where claims development data of different calendar years are stacked into separate observation vectors.…”