Insurance Reserve Intelligence Platform

Anugya A; Saket Mohanty; Abhilash Timmapur; Somya Rai

cs.AISep 25, 2026

Insurance Reserve Intelligence Platform

Authors: Anugya A, Saket Mohanty, Abhilash Timmapur, Somya Rai

Organizations: EXL Service

Abstract

Insurance reserve estimation is a fundamental actuarial task supporting premium pricing, solvency assessment, financial reporting, capital planning, and risk management. Classical reserve methods based on Thiele's differential equation provide a rigorous and interpretable foundation for life insurance valuation, but repeated reserve calculations become computationally expensive in sensitivity analysis, optimization, and large-scale scenario evaluation. This paper presents an Insurance Reserve Intelligence Platform for term-life reserve modelling that combines a classical Thiele-equation solver with a Physics-Informed Neural Network (PINN) enhanced by Knowledge-Informed Neural Network (KINN) losses. The framework includes synthetic policy generation, risk-adjusted premium calculation, classical reserve trajectory generation, reserve-ratio dataset construction, configurable neural training, validation diagnostics, sensitivity and elasticity analysis, prototype optimization workflows, and interest-rate scenario testing. A key refinement is the use of premium ratio and the explicit separation of pricing-time and scenario-time interest-rate semantics. The final model uses seven features: elapsed time, issue age, pricing interest rate, scenario interest rate, premium ratio, sum assured, and mortality intensity. It predicts a standardized reserve ratio instead of raw reserve values, improving numerical stability across policies with different sums assured. The model achieved an R2 of 0.9887, MAE of 785.48, and RMSE of 1212.76 on the test set. On 200 policies, PINN/KINN inference was approximately 119.53 times faster than the classical solver. Results show strong predictive accuracy, physics consistency, and boundary performance, while highlighting remaining limitations in monotonicity and out-of-distribution generalization.

Figures & tables

Attribute	Value
Training policies	1000
Validation policies	200
Test policies	200
Time steps per policy	48
Issue age range	25 to 70
Policy term range	5 to 30 years

Table 1: Dataset and policy generation configuration.

Statistic	Value
Minimum reserve	-23,714.75
Maximum reserve	79,262.70
Mean reserve	6,445.48
Standard deviation	11,408.39

Table 2: Reserve distribution statistics from the generated dataset.

Figure 1: Exploratory data analysis of the synthetic term-life portfolio showing peak reserve against issue age. The colour scale represents policy term, indicating how age and contract duration jointly affect reserve levels.

Parameter	Value
Interest-rate mean	0.03992010
Interest-rate standard deviation	0.01476313
Premium-ratio mean	0.00470961
Premium-ratio standard deviation	0.00367158
Target mean	0.00800405
Target standard deviation	0.01264168

Table 3: Feature and target normalization statistics.

Attribute	Value
Input dimension	7
Hidden dimension	256
Number of layers	6
Activation function	$\tanh$
Dropout	0.0
Skip connections	Enabled

Table 4: Network architecture and training configuration.

Panel of Figure 2 — Figure 2: Loss framework used to train the PINN/KINN reserve model.

Panel of Figure 3 — Figure 3: Overall architecture of the Insurance Reserve Intelligence Platform.

Metric	Value
Mean Squared Error (MSE)	1,470,771.88
Mean Absolute Error (MAE)	785.48
Root Mean Squared Error (RMSE)	1,212.76
Coefficient of Determination ( $R^{2}$ )	0.9887

Table 5: Final prediction performance on the test dataset.

Figure 4: Comparison between reserve trajectories predicted by the PINN/KINN model and the classical Thiele solver.

Diagnostic	Value
Accuracy score	76 / 100
Physics score	99 / 100
Boundary condition score	89 / 100
Actuarial monotonicity score	27 / 100
Generalization score	0 / 100
Mean relative error	4.8%

Table 6: Validation diagnostic summary.

Figure 5: Validation report summarizing accuracy, PDE residual behaviour, boundary error, monotonicity, and generalization.

Metric	Value
Hardware environment	NVIDIA T4 GPU, 4 vCPUs, 16 GiB RAM
Number of policies	200
Classical solver total time	1.652123 s
PINN/KINN total time	0.013822 s
Classical solver time per policy	8.2606 ms
PINN/KINN time per policy	0.0691 ms

Table 7: Runtime benchmark for reserve evaluation on 200 policies.

Sensitivity	Value	Interpretation
$dV/dr$	-6,500.754	Correct sign for interest-rate reserve response
$dV/d\mu$	-817,044.188	Incorrect sign for mortality response
$dV/d(P/S)$	225,128.984	Correct positive premium-ratio response
$dV/dS$	approximately 0.000	Positive but very small response

Table 8: Reference-policy sensitivity results.

Figure 6: Reference-policy sensitivity analysis using one-variable-at-a-time perturbations.

Variable	Elasticity	Sign assessment
Premium ratio	+267.92%	Correct
Interest rate	-142.12%	Correct
Mortality	-112.63%	Incorrect
Sum assured	+76.03%	Correct

Table 9: Reference-policy elasticity results.

Figure 7: Reserve elasticity analysis showing relative reserve response to one-percent changes in each feature.

Experiment	Initial reserve	Final reserve	Observation
Pricing optimization	approx 11,410	approx 11,140	Smooth convergence and stabilization
Product-design optimization	approx 11,430	approx 10,720	Stepwise convergence within early iterations
Portfolio optimization	approx 85,000	approx 76,500	Gradual portfolio-level reserve reduction

Table 10: Optimization convergence observations from result plots.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$t$	Elapsed policy duration
$T$	Policy term or maturity time
$a$	Issue age
$V(t)$	Reserve at time $t$
$P$	Premium
$S$	Sum assured or death benefit

Appendix

Table 11: Main variables used in the paper.

Constraint	Purpose
Boundary condition	Enforces the terminal reserve condition $V(T)=0$ .
Monotonicity	Encourages actuarially consistent reserve behaviour with respect to mortality, premium, interest rate, and sum assured.
Reserve positivity	Discourages strongly negative reserve values under normal policy conditions.
Reserve ceiling	Prevents reserves from exceeding reasonable actuarial limits without justification.
Smoothness	Reduces unrealistic oscillations in reserve trajectories.
Scenario constraints	Improves reserve behaviour under varying interest-rate environments using scenario and peak losses.

Appendix

Table 12: Knowledge-informed constraints incorporated during training.

Stage	Problem	Main Fix
Runs 1–3	Raw reserves caused unstable training	Standardized reserve-ratio target
Runs 4–8	No systematic validation and unstable PDE loss	Added validation dashboard and reformulated PDE in reserve-ratio space
Runs 9–15	Sensitivities were difficult to interpret and premium dominated learning	Added sensitivity/elasticity analysis and replaced premium with premium ratio
Runs 16–21	Need optimization and stronger interest-rate scenario behaviour	Added prototype optimization workflows, pricing/scenario rate semantics, scenario loss, and peak-reserve loss

Appendix

Table 13: Summary of major development stages.

Neural Surrogate Modeling

Neural surrogate modeling uses learned models to approximate costly simulations, enabling faster prediction, design, control, and inference.

See all 412 papers

Insurance Pricing Optimization via Off-Policy Evaluation
May 27, 2026Sascha Günther, Dimitri Semenovich, Mario V. WüthrichOff-Policy Evaluation Policy Optimization
Department of Mathematics, ETH Zurich
LSTM-Based Detection of Structural Breaks in Property Insurance Loss Reserving: A Climate-Informed Approach
Jun 9, 2026Thomas Mbrice, Shashwat PanigrahiRecurrent Neural Networks Change-Point Detection
Stony Brook University · Department of Computer Science
Is TabPFN the Silver Bullet for Insurance Pricing?
May 21, 2026Bruno Deprez, Wouter Verbeke, Tim VerdonckTabular Foundation Models Tabular ICL
KU Leuven · University of Antwerp-imec

May 27, 2026J/K move · Enter open · S save

Insurance Pricing Optimization via Off-Policy Evaluation

Sascha Günther, Dimitri Semenovich, Mario V. Wüthrich

Department of Mathematics, ETH Zurich

Off-Policy Evaluation Policy Optimization

Open paper AskPDF arXiv

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space and yields variance reduction compared to the classical inverse propensity score estimator. Building on these value estimates, we investigate policy optimization and present two practical approaches for computing optimal pricing rules: an interpretable data-shared Lasso formulation and a flexible policy parameterization based on neural networks. Using a controlled synthetic travel insurance environment, we empirically confirm the theoretical results and show that neural networks outperform existing techniques for policy optimization.

Abstract

Neural Surrogate Modeling

Explore similar work

Insurance Pricing Optimization via Off-Policy Evaluation

LSTM-Based Detection of Structural Breaks in Property Insurance Loss Reserving: A Climate-Informed Approach

Is TabPFN the Silver Bullet for Insurance Pricing?