Theoretical and numerical Analysis on Optimal dividend policy of an insurance company with positive transaction cost and higher solvency

Zongxia Liang; Jicheng Yao

Home/Archive/arXiv

arXiv · 1005.1356

Theoretical and numerical Analysis on Optimal dividend policy of an insurance company with positive transaction cost and higher solvency

Zongxia Liang·Jicheng Yao

View original source ↗Read source document ↗Export metadata ↓

Abstract

Based on a point of view that solvency and security are first, this paper considers regular-singular stochastic optimal control problem of a large insurance company facing positive transaction cost asked by reinsurer under solvency constraint. The company controls proportional reinsurance and dividend pay-out policy to maximize the expected present value of the dividend pay-outs until the time of bankruptcy. The paper aims at deriving the optimal retention ratio, dividend payout level, explicit value function of the insurance company via stochastic analysis and PDE methods. The results present the best equilibrium point between maximization of dividend pay-outs and minimization of risks. The paper also gets a risk-based capital standard to ensure the capital requirement of can cover the total given risk. We present numerical results to make analysis how the model parameters, such as, volatility, premium rate, and risk level, impact on risk-based capital standard, optimal retention ratio, optimal dividend payout level and the company's profit.

Explore related subjects

q-fin.RM math.OC math.PR

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Zongxia Liang, Jicheng Yao. 2010-12-21. Theoretical and numerical Analysis on Optimal dividend policy of an insurance company with positive transaction cost and higher solvency. https://arxiv.org/abs/1005.1356

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Risk-minimizing reinsurance with adverse selection

This paper provides a comprehensive characterization of optimal reinsurance mechanisms under adverse selection when a monopolistic reinsurer faces a continuum of insurers with multi-dimensional private information on loss exposures and Value-at-Risk (VaR) preferences. Moving beyond standard single-dimensional or discrete-type models, we resolve an infinite-dimensional, non-convex screening problem by introducing a novel pre-reinsurance VaR reparameterization and an indirect utility representation. This framework converts global incentive constraints into tractable, typewise conditions. Using a Breeden-Litzenberger representation, we show that optimal indirect utility consistently adopts a hinge form across stop-loss, quota-share, and change-loss contract classes, yielding an endogenous market-exclusion threshold. Among participating types, stop-loss contracts screen via type-dependent deductibles, whereas quota-share contracts induce complete pooling at full coverage. Moreover, under mild conditions, expanding the contract space to change-loss policies yields no extra profit beyond optimal stop-loss designs. Numerical examples further illustrate the fundamental economic trade-off between extracting information rents and excluding low-exposure types. Our approach provides deeper insight into the mechanisms of discrimination and exclusion in reinsurance markets characterized by asymmetric information, enriching theoretical and practical perspectives on contract design in the presence of adverse selection.

q-fin.RM↗

arXiv2026

Quantifying the 2027 Solvency II Risk Margin Reform

The 2027 Solvency II reform recalibrates the Risk Margin by reducing the prescribed cost-of-capital rate from 6% to 4.75% and introducing a time-dependent attenuation of future Solvency Capital Requirements. This paper develops an analytical and numerical framework for characterizing the effect of the final regulatory calibration. By normalizing discounted projected capital requirements into a probability distribution over run-off time, we obtain an exact representation of the ratio between the revised and previous Risk Margins. The framework yields sharp universal and horizon-specific bounds, characterizes the effect of later capital timing through stochastic dominance, and shows that mean run-off time alone does not determine the reform effect when temporal dispersion varies. Additional bounds are derived conditional on mean run-off time and horizon. Conditional on a given projected SCR path, the mechanical reduction lies between 20.83% and 60.42%. For proportional Best Estimate projections, an exact covariance decomposition identifies how departures from proportionality affect the relative reform ratio. Holding the projected SCR path fixed, the revised formula has a lower direct interest-rate semi-elasticity than the previous calibration. A reduced-form stochastic extension further quantifies convexity effects arising from uncertainty in capital persistence. Numerical applications reconstruct Risk Margin calculations from published actuarial run-off profiles and complement them with controlled long-horizon, interest-rate, and persistence experiments. The results show that the reform effect is governed by the temporal structure of future capital and provide tractable tools for assessing projected capital profiles, Risk Margin simplifications, and direct discount-rate sensitivity.

q-fin.RM↗

arXiv2026

Towards foundation models for insurance risk modelling

Claim narratives, images and sensor data contain information about insured risks that is difficult to use through existing actuarial models. Foundation models learn patterns from large datasets before being adapted to particular tasks. By turning these high-dimensional sources into variables or numerical representations, they could help insurers use more of the information they already collect, potentially reducing the experience needed to develop each application. For example, a language model could identify a worsening injury in a new claim note, allowing a reserving model to recognise the change in expected cost before the payments reveal the deterioration. In this paper, we review language, vision, geospatial, time series, tabular and scientific models, explaining existing insurance applications and potential future uses. Scientific models extend this approach to future weather and climate conditions: their simulations can inform loss estimates once local hazards are linked to asset damage, repair costs and insurance coverage. We propose a process to connect these model outputs to actuarial calculations and to assess their predictive contribution, stability and compliance with rules on information use. Evaluating these applications is difficult when final claim costs become known only after long delays, large losses are rare or patterns learned elsewhere fail to transfer to the target portfolio. Richer data can reveal private information and support finer risk classification, which can change access to insurance. Reusing the same models across insurers also creates dependence on shared predictions and providers.

q-fin.RM↗