From Explaining to Enabling: Actionable Transparency in Algorithmic Insurance Pricing

Agathe Fernandes Machado; Fei Huang

cs.LGOct 25, 2026

From Explaining to Enabling: Actionable Transparency in Algorithmic Insurance Pricing

Authors: Agathe Fernandes Machado, Fei Huang

Organizations: Département de Mathématiques, Université du Québec à Montréal, Montréal (UQAM), Québec, Canada · School of Risk and Actuarial Studies, UNSW Business School, UNSW, Sydney, New South Wales, Australia

Abstract

Machine learning (ML) systems increasingly make consequential decisions about individuals, including credit, hiring, and insurance. Research on ML-driven insurance pricing has asked how the pricing mechanism itself can be made accountable. Yet it remains unclear how an individual policyholder's algorithmically determined premium should be explained to them. We argue that a useful explanation must be valid, actionable, and reliable. A valid recommendation lowers the premium according to the model. An actionable recommendation changes only characteristics the policyholder can control. A reliable recommendation has an actual outcome that is likely to meet the target, even in sparsely observed regions of the feature space where the model is uncertain. We formalize these three requirements as axioms and develop a method that turns an algorithmic premium into recommendations that meet them. The method meets the third requirement with a Conformal Prediction constraint, which screens out recommendations that the model is too uncertain about and thereby bounds the rate of unreliable recommendations. We apply four Counterfactual Explanation techniques to 57,832 real Florida flood-insurance claims and 98,058 synthetic driver-telematics policies. We adapt these techniques for insurance applications, so that their recommendations change only controllable characteristics and resemble policyholders observed in the data. In our illustrations, the constrained recommendations for high-risk policyholders are both more reliable and associated with larger predicted risk reductions than the unconstrained ones. These results suggest that insurers can give policyholders explanations that are both actionable and trustworthy. The work contributes to research on algorithmic accountability and offers implications for insurers and regulators.

Figures & tables

	Axiom 1	Axiom 2	Axiom 3		Desirable properties
Method	Valid.	Action.	Reliab.		Plausib.	Causal.	Multip.
			Uncon.	CP filter
WhatIf ( Wexler et al. 2020 )	✓	✓ †	$\times$	(✓) †	✓	$\times$	✓
NICE ( Brughmans et al. 2023 )	✓	✓ †	$\times$	(✓) †	✓	$\times$	✓
MOC ( Dandl et al. 2020 )	(✓)	✓	$\times$	(✓) †	✓	$\times$	✓
DiCE ( Mothilal et al. 2020 )	✓	✓	$\times$	(✓) †	✓ †	$\times$	✓

Table 1: The four retained Counterfactual Explanation techniques against the three axioms (validity, actionability, reliability) and three desirable properties (plausibility, causality, multiplicity), after our extensions. “Uncon.” denotes the unconstrained version of each technique. All four handle regression. ✓ indicates that the property holds, (✓) that it holds only through a post-hoc filter and not through the search, and

\times

that it is not guaranteed.

\dagger

marks a property added by this paper relative to the technique’s published implementation (Appendix C ), namely actionability for WhatIf and NICE and plausibility through a post-hoc filter for DiCE. The CP filter column applies the CP constraint of Equation 2 , and may return no instance when the hard constraint is infeasible. Axiom 3 then holds by Theorem 3.3 .

Method	Search strategy	Main strengths	Main limitations
WhatIf	Returns the $M$ closest training instances whose prediction lies in the target range	Plausible and valid by construction, and by far the fastest	Cannot recommend a change absent from the training data, and is less sparse than NICE and MOC
NICE	Starts from a nearby valid training instance and moves toward it one feature at a time	Sparse recommendations, valid by construction, and the highest share of reliable recommendations in our sample	Tied to its starting instance, and most of its recommendations are also found by WhatIf and MOC
MOC	Genetic algorithm (NSGA-II) that optimizes validity, proximity, sparsity, and plausibility jointly	Closest, sparsest, and most plausible recommendations in our sample, and can propose changes not observed in the data	Validity is not guaranteed by the search, very few recommendations are reliable, and the algorithm needs tuning
DiCE	Optimizes diversity across the $M$ recommendations	Largest and most diverse set of recommendations, and valid within the search	Highest distance and sparsity in our sample, needs a post-hoc plausibility filter, and is implemented in Python

Table 2: Features, strengths, and limitations of the four retained CE techniques.

Panel of Figure 1 — Figure 1: Counterfactual explanations generated by the WhatIf technique for a high-risk (outlier) query instance, without (left) and with (right) the reliability constraint formalized in Section 3.4 . The background shading represents estimated predictive uncertainty. Without the constraint, recommended counterfactuals remain in the same high-uncertainty region as the query instance, purely because that region minimizes proximity. With the constraint, recommendations are relocated toward regions in which the model’s own confidence is higher.

Method	How the CP constraint is incorporated
WhatIf	Candidate set $\mathcal{D}_{\text{train}}^{\prime}$ additionally requires $\sup(\widehat{C}_{1-\alpha}(\boldsymbol{x}^{\prime}))\leq y^{u}$
NICE	Post-hoc filter over generated candidates
MOC	Post-hoc filter over generated candidates
DiCE	Post-hoc filter over generated candidates

Table 3: How the CP reliability constraint (Axiom 3 ) of Equation 2 is incorporated into each of the four CE techniques of Table 1 .

Query	CE	basement	elevation	contents_loc	Pred.	CP constr.	CP bound
$\boldsymbol{x}_{1}$	$\boldsymbol{x}^{\prime}_{1,1}$	0	yes	Lowest_floor_only	0.38	$\times$	0.64
	$\boldsymbol{x}^{\prime}_{1,2}$	0	no	Lowest_floor_and_above	0.31	$\times$	0.56
	$\boldsymbol{x}^{\prime}_{1,3}$	0	yes	Lowest_floor_and_above	0.27	✓	0.52
	$\boldsymbol{x}^{\prime}_{1,4}$	1	yes	Lowest_floor_only	0.21	✓	0.45
$\boldsymbol{x}_{2}$	$\boldsymbol{x}^{\prime}_{2,1}$	0	yes	Lowest_floor_only	0.34	$\times$	0.58
	$\boldsymbol{x}^{\prime}_{2,2}$	3	yes	Lowest_floor_only	0.27	$\times$	0.51

Table 4: Actionable, uncertainty-aware Counterfactual Explanations for flood severity reduction, for two query policyholders

\boldsymbol{x}_{1}

and

\boldsymbol{x}_{2}

. Changed actionable feature values are shown in bold. “Pred.” is the predicted loss ratio. “CP constr.” indicates whether the soft CP reliability constraint is considered when selecting the counterfactual instance. “CP bound” is the 80%-confidence upper bound of predicted severity for the recommended counterfactual.

Figure 2: Decision plot for policyholder

\boldsymbol{x}_{2}

. The plot shows the recommended changes in actionable features to reach the four counterfactual instances (

\boldsymbol{x}^{\prime}_{2,1}

\boldsymbol{x}^{\prime}_{2,2}

\boldsymbol{x}^{\prime}_{2,3}

, and

\boldsymbol{x}^{\prime}_{2,4}

of Table 4 ), along with their corresponding predicted flood severity. Each line starts from the query values of

\boldsymbol{x}_{2}

(black) and follows one counterfactual across the three actionable features to its predicted value (right axis).

CE	Pct.drive.rush	Accel.14miles	Brake.14miles	Pred.	CP constr.	CP bound
$\boldsymbol{x}^{\prime}_{1}$	mostly_pm	no	yes	18%	$\times$	35%
$\boldsymbol{x}^{\prime}_{2}$	mostly_pm	no	no	12%	$\times$	24%
$\boldsymbol{x}^{\prime}_{3}$	none	yes	no	10%	✓	20%
$\boldsymbol{x}^{\prime}_{4}$	mostly_am	no	no	7%	✓	18%

Table 5: Actionable, uncertainty-aware Counterfactual Explanations for claim frequency reduction, for a query policyholder with predicted frequency 22% and 80%-confidence CP upper bound 39%. Changed actionable feature values are shown in bold. “Pred.” is the predicted claim frequency. “CP constr.” indicates whether the CP reliability constraint is applied. “CP bound” is the 80%-confidence upper bound of predicted frequency for the recommended counterfactual.

Figure 3: Decision plot for a query policyholder in the telematics dataset. The plot shows the recommended changes in actionable features to reach the four counterfactual instances of Table 5 , along with their corresponding predicted claim frequency. Each line starts from the query values (black) and follows one counterfactual across the three actionable features to its predicted value (right axis).

Query	CE	CP constr.	Features changed	Frequency reduction
$\boldsymbol{x}$	$\boldsymbol{x}^{\prime}_{1}$	$\times$	1.00	18.2%
	$\boldsymbol{x}^{\prime}_{2}$	$\times$	2.00	45.5%
	$\boldsymbol{x}^{\prime}_{3}$	✓	2.00	54.5%
	$\boldsymbol{x}^{\prime}_{4}$	✓	3.00	68.2%
$\mathcal{D}_{\text{test}}$	WhatIf	$\times$	1.43	26.2%
	WhatIf	✓	2.73	61.6%

Table 6: Predicted frequency reduction relative to the query instance’s own prediction, by whether the CP reliability constraint (“CP constr.”) is applied, illustrating the proximity-cost pattern characterized by Proposition 3.4 . Rows related to

\boldsymbol{x}

show the changes from Table 5 , while the others show instance-weighted averages over

\mathcal{D}_{\text{test}}

. The bold rows give the overall averages.

	Axioms		Desirable properties				Computation and overlap
Method	Valid.	Reliab.	Plausib.	Prox.	Sparsity	$M$	Time	Shared	Dup.
WhatIf	100%	3.34%	0.008	0.164	1.48	4.34	0.04	48%	1
NICE	100%	3.78%	0.008	0.135	1.22	1.42	2.46	94%	1
MOC	74%	0.23%	0.003	0.122	1.09	1.37	0.71	74%	1
DiCE	100%	2.98%	0.013	0.177	1.60	5.15	2.32	0%	6.34

Table 7: Global evaluation of Counterfactual Explanation (CE) methods on 1,000 samples from the telematics test set. Valid. and Reliab. correspond to Axioms 1 and 3 . Plausibility (“Plausib.”) is the Gower distance to the closest instance in

\mathcal{D}_{\text{train}}

. Proximity (“Prox.”) is the Gower distance to the query instance. Sparsity is the number of changed features. Validity (“Valid.”) is the percentage of valid CEs. Reliability is the percentage of reliable CEs at an 80% confidence level. “Time” is the average execution time, in second, per query. “Shared” is the percentage of CEs found in the three other methods. “Dup.” is the average number of duplicate CEs per query, and

M

is the average multiplicity per query.

Method	$\alpha$	Proportion reliable	$\Delta_{\text{proximity}}$	$\Delta_{\text{sparsity}}$	$\Delta_{\text{frequency}}$
WhatIf	0.20	3.34%	0.118	1.06	24.9%
WhatIf	0.05	1.04%	0.135	1.22	24.6%
NICE	0.20	3.78%	0.151	1.36	27.0%
NICE	0.05	1.08%	0.175	1.57	27.3%
MOC	0.20	0.23%	0.167	1.50	25.6%
MOC	0.05	0.08%	0.167	1.50	29.2%

Table 8: Illustration of the proximity and sparsity costs (

\Delta_{\text{proximity}}

\Delta_{\text{sparsity}}

) and the frequency reduction (

\Delta_{\text{frequency}}

) resulting from the addition of the hard reliability constraint, for different values of the Conformal Prediction interval coverage level

\alpha

, averaged over 1,000 randomly drawn samples from the telematics test set.

\Delta

denote the average difference between constrained and unconstrained counterfactuals, and is it computed only over instances from with a reliable CE.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 12 — Figure A1: Taxonomy of machine learning interpretability methods, following Molnar (2025) . The bold path is the post-hoc, model-agnostic, local branch to which this paper’s requirements narrow attention.

Method	Type	Category	Summary	Limitation for Policyholder Communication
PDP ( Friedman 2001 )	global	plot	Marginal effect of a feature on model predictions	Reports model-level, not individual-level, information; assumes feature independence
ALE ( Apley and Zhu 2020 )	global	plot	Similar to PDP but accounts for feature correlations	Still model-level, not individual-level
PFI ( Breiman 2001 , Fisher et al. 2019 )	global	importance	Change in model performance when a feature is permuted	Model-level; reports importance, not actionable direction, for any individual
ICE ( Goldstein et al. 2015 )	local	plot	Individual-level analogue of PDP	Graphical, not contrastive; assumes feature independence; not easily read by lay users
LIME ( Ribeiro et al. 2016 )	local	surrogate model	Locally approximates predictions with an interpretable model	Reports feature contributions, not the change needed to reach a different outcome; sampling methods can ignore feature dependencies
SHAP ( Lundberg and Lee 2017 )	local	importance	Attributes a prediction to features via cooperative game theory	Answers “why this value,” not “what would change it”; computationally costly; can mislead under feature dependence

Appendix

Table A1: Comparison of post-hoc, model-agnostic interpretability methods on their suitability for individual-level, actionable policyholder communication.

Variable	Type	Actionability	Description
basement	categ.	✓	Type of the lowest enclosed area of the building.
elevation	categ.	✓	Indicates whether the building has been constructed according to NFIP criteria for an elevated building, i.e., whether the lowest floor is raised above the expected flood level and supported by an appropriate foundation system.
contents_loc	categ.	✓	Location of the contents within the insured building.
nb_floors	num.	$\times$	Number of floors in the insured building.
non_profit	categ.	$\times$	Indicates whether the building is reported as a non-profit property in the policy application.
occupancy	categ.	$\times$	Use and occupancy type of the insured structure.

Appendix

Table A2: Description and actionability of the variables used in the flood claim severity study of Section 4 .

Feature	Contribution	Cumulative contribution
baseline	$\times$	0.3175
basement 0	-0.0407	0.2768
building_age	0.0272	0.3040
damage_cause 4	0.0227	0.3267
basement 3	0.0183	0.3450
damage_cause 1	0.0174	0.3624

Appendix

Table A3: SHAP feature contributions for the 10 most important features on

\boldsymbol{x}_{2}

. Positive contributions increase the predicted value and negative ones decrease it. Features in bold are actionable.

Feature	Feature weight
intercept	0.1842
basement 3	0.1935
building_age	0.0110
contents_location Mobile_home	0.0110
nb_floors 3	-0.0102
non_profit	0.0098

Appendix

Table A4: LIME feature weights for the 10 most important features on

\boldsymbol{x}_{2}

. Positive weights increase the predicted value and negative ones decrease it. Features in bold are actionable.

	Axioms			Desirable properties			Applicability
Method	Valid.	Action.	Reliab.	Plausib.	Causal.	Multip.	Regr.	Categ.	Code
FACE ( Poyiadzi et al. 2020 )	✓	✓	$\times$	✓	$\times$	$\times$	$\times$	$\checkmark$	Python
Prototype ( Van Looveren and Klaise 2021 )	✓	✓	$\times$	✓	$\times$	$\times$	$\times$	✓	Python
MOC ( Dandl et al. 2020 )	(✓)	✓	$\times$	✓	$\times$	✓	✓	✓	R
GeCo ( Schleich et al. 2021 )	✓	✓	$\times$	✓	✓	✓	$\times$	✓	Python
Sequential AR ( Verma et al. 2022 )	✓	✓	$\times$	✓	✓	✓	$\times$	✓	Python

Appendix

Table A5: Comparison of representative CE techniques from the wider literature against properties relevant to insurance pricing. Validity, actionability, and reliability correspond to Axioms 1 , 2 , and 3 . Plausibility, causality, and multiplicity are desirable properties. Regression (“Regr.”), categorical variables (“Categ.”), and public code (“Code”) describe applicability. “Categ.” indicates whether the technique handles categorical variables. ✓ indicates the property is satisfied, (✓) that validity is obtained only through a post-hoc filter,

\times

that it is not satisfied, and . that the information was not found or is unavailable in the source publication. For reliability,

\times

means that we found no mechanism in the source publication that bounds the rate of unreliable recommendations.

Parameter	Approach	Description	Value
$\epsilon$	WhatIf	Neighborhood of immutable numerical features used to select instances for actionability	0.3 (default value)
$R$	NICE	Reward function for generated counterfactuals	Plausibility criterion
$\delta$	NICE	Accepted margin for considering a prediction as correct	Half the median absolute error (default value)
$k$	MOC	Number of data points used for the plausibility objective	1 (default value)
$\mu$	MOC	Population size of the genetic algorithm	5
$n_{\text{gen}}$	MOC, DiCE	Number of generations in the genetic algorithm	10

Appendix

Table A6: Description and values of the hyperparameters used for the counterfactual explanation techniques in the experiments of Section 4 .

Variable	Type	Actionability	Description
Duration	num.	$\times$	Duration of the insurance coverage of the policy, in days.
Insured.age	num.	$\times$	Age of the insured driver, in years.
Insured.sex	categ.	$\times$	Sex of the insured driver.
Car.age	num.	$\times$	Age of the vehicle, in years.
Credit.score	num.	$\times$	Credit score of the insured driver.
Region	categ.	$\times$	Type of region where the driver lives: rural or urban.

Appendix

Table A7: Description and actionability of the variables used in the telematics frequency study of Section 4.2 . “mph/s” denotes miles per hour per second.

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