Log normal claim models with common shocks

TL;DR

This paper introduces a flexible multiplicative log-normal model for multiple claim arrays affected by common shocks, simplifying parameter estimation and addressing unbalanced shocks in prior additive models.

Contribution

It proposes a novel multiplicative structure for claim models with common shocks, enabling linear regression-based estimation and handling unbalanced shocks effectively.

Findings

Closed-form solutions for location parameters.

Simplified estimation via linear regression.

Accommodates unbalanced shocks in claim data.

Abstract

This paper is concerned with modelling multiple claim arrays that are subject to one or more common shocks. It uses a structure that involves very general forms both idiosyncratic and common shock components of cell means. The dependencies between arrays, or between cells within an array, generated by the shocks are also of very general form. All of this appears in the prior literature, where the idiosyncratic and shock components are additive. This has created the awkwardness of unbalanced shocks. The present paper rectifies this by defining these components as multiplicative. Observations in individuals cells of claim arrays are assumed log normal (later log Tweedie) in order to accommodate the multiplicativity. Conveniently, the log normal case reduced parameter estimation to linear regression, yielding closed form solution of location parameters, and even of dispersion parameters in some cases.