Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Investment-Driven Insurance Pricing and Liquidity Management

Bingzheng Chen, Jan Dhaene, Chun Liu, Shunzhi Pang

Abstract

This paper develops a dynamic equilibrium model of the insurance market that jointly characterizes insurers' underwriting, investment, recapitalization, and dividend policies under model uncertainty and financial frictions. Competitive insurers maximize shareholder value under a subjective worst-case probability measure, giving rise to liquidity-driven underwriting cycles and flight-to-quality behavior. While an equilibrium typically fails to exist in such dynamic liquidity management framework with external financial investment, we show that incorporating model uncertainty restores equilibrium existence under plausible parameter conditions. Moreover, the model uncovers a novel relationship between the correlation of insurance and financial market risks and the equilibrium insurance price: negative loadings may emerge when insurance gains and financial returns are positively correlated, contrary to conventional intuition.

Robust Investment-Driven Insurance Pricing and Liquidity Management

Abstract

This paper develops a dynamic equilibrium model of the insurance market that jointly characterizes insurers' underwriting, investment, recapitalization, and dividend policies under model uncertainty and financial frictions. Competitive insurers maximize shareholder value under a subjective worst-case probability measure, giving rise to liquidity-driven underwriting cycles and flight-to-quality behavior. While an equilibrium typically fails to exist in such dynamic liquidity management framework with external financial investment, we show that incorporating model uncertainty restores equilibrium existence under plausible parameter conditions. Moreover, the model uncovers a novel relationship between the correlation of insurance and financial market risks and the equilibrium insurance price: negative loadings may emerge when insurance gains and financial returns are positively correlated, contrary to conventional intuition.
Paper Structure (19 sections, 3 theorems, 38 equations, 9 figures, 2 tables)

This paper contains 19 sections, 3 theorems, 38 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Insurance Market
  4. Financial Investment Opportunity
  5. Optimization Objective
  6. Equilibrium Solution
  7. Internal Financing Region
  8. External Financing and Payout Regions
  9. Robust Equilibrium
  10. Quantitative Analysis
  11. Comparison of Equilibria with and without Financial Investment
  12. Impact of Correlation Coefficient
  13. Impact of Robustness Degree
  14. Impact of Financing Cost
  15. Insurers’ Long-Run Behavior Pattern
  16. ...and 4 more sections

Key Result

Proposition 1

In the presence of model uncertainty, suppose that Assumptions Assumption market-to-book ratio and Assumption Robust hold and that the following system of equations admits a solution for $p^{\ast}(M)$ and $u^{\ast}(M)$ on $[\underline{M}, \overline{M}]$: subject to the boundary conditions: $u(\underline{M}) = 1 + \gamma$, $u(\overline{M}) = 1$, $u^{\prime}(\underline{M}) = u^{\prime}(\overline{M}

Figures (9)

  • Figure 4.1: Equilibrium Outcomes with and without Financial Investment.
  • Figure 4.2: Optimal Density Generators with and without Financial Investment.
  • Figure 4.3: Equilibrium Outcomes for Different Correlation Coefficient $\rho$.
  • Figure 4.4: Equilibrium Outcomes for Different Robustness Degree $\theta$.
  • Figure 4.5: Equilibrium Outcomes for Different Financing Cost $\gamma$.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Proposition 1: Robust Equilibrium with Model Uncertainty
  • Remark 1
  • Proposition 2
  • Proposition 3