Valuation of Non-Life Liabilities from Claims Triangles

Lindholm, Mathias; Lindskog, Filip; Wahl, Felix

doi:10.3390/risks5030039

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Θ can be chosen to reflect parameter uncertainty. To illustrate how such a choice may be implemented, consider the regression estimators from Lindholm et al [18] based on data from accident years i = i 0 , . .…”

Section: Gaussian Examplementioning

confidence: 99%

Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

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We study market-consistent valuation of liability cash flows motivated by current regulatory frameworks for the insurance industry. Building on the theory on multiple-prior optimal stopping we propose a valuation functional with sound economic properties that applies to any liability cash flow. Whereas a replicable cash flow is assigned the market value of the replicating portfolio, a cash flow that is not fully replicable is assigned a value which is the sum of the market value of a replicating portfolio and a positive margin. The margin is a direct consequence of considering a hypothetical transfer of the liability cash flow from an insurance company to an empty corporate entity set up with the sole purpose to manage the liability run-off, subject to repeated capital requirements, and considering the valuation of this entity from the owner's perspective taking model uncertainty into account. Aiming for applicability, we consider a detailed insurance application and explain how the optimisation problems over sets of probability measures can be cast as simpler optimisation problems over parameter sets corresponding to parameterised density processes appearing in applications.

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Section: Gaussian Examplementioning

confidence: 99%

Multiple-prior valuation of cash flows subject to capital requirements

Engsner¹,

Lindskog²,

Thoegersen³

2021

Preprint

Self Cite

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show abstract

“…For more on other models than the distribution free Chain-Ladder model that are used in an insurance context, see e.g. Kremer (1984) and Lindholm et al (2017).…”

Section: Examplesmentioning

confidence: 99%

On the variance parameter estimator in general linear models

Lindholm

Wahl

2019

Metrika

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In the present note we consider general linear models where the covariates may be both random and non-random, and where the only restrictions on the error terms are that they are independent and have finite fourth moments. For this class of models we analyse the variance parameter estimator. In particular we obtain finite sample size bounds for the variance of the variance parameter estimator which are independent of covariate information regardless of whether the covariates are random or not. For the case with random covariates this immediately yields bounds on the unconditional variance of the variance estimator-a situation which in general is analytically intractable. The situation with random covariates is illustrated in an example where a certain vector autoregressive model which appears naturally within the area of insurance mathematics is analysed. Further, the obtained bounds are sharp in the sense that both the lower and upper bound will converge to the same asymptotic limit when scaled with the sample size. By using the derived bounds it is simple to show convergence in mean square of the variance parameter estimator for both random and non-random covariates. Moreover, the derivation of the bounds for the above general linear model is based on a lemma which applies in greater generality. This is illustrated by applying the used techniques to a class of mixed effects models.Keywords General linear models · Non-Gaussian error terms · Moments of variance parameter estimators · Finite sample size bounds · Random covariates · Unconditional bounds The general linear modelThe primary model class that will be analysed is defined as follows: Let y be a random n × 1 vector and let X be a random n × p x matrix of almost surely full column rank,

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Explicit moments for a class of micro-models in non-life insurance

Wahl

2019

Insurance: Mathematics and Economics

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Valuation of Non-Life Liabilities from Claims Triangles

Cited by 6 publications

References 14 publications

Multiple-prior valuation of cash flows subject to capital requirements

Multiple-prior valuation of cash flows subject to capital requirements

On the variance parameter estimator in general linear models

Explicit moments for a class of micro-models in non-life insurance

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