Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Investment-Driven Insurance Pricing under Correlation Ambiguity

Shunzhi Pang

Abstract

As insurers increasingly behave like financial intermediaries and actively participate in capital markets, understanding the dependence structure between insurance and financial risks becomes crucial for insurers' operations. This paper studies dynamic equilibrium insurance pricing when insurers face ambiguity about the correlation between insurance and financial risks and optimally choose underwriting and investment strategies under worst-case beliefs. Correlation ambiguity can generate multiple equilibrium regimes. Contrary to conventional intuition, we find ambiguity does not necessarily increase insurance prices nor reduce insurers' utility.

Robust Investment-Driven Insurance Pricing under Correlation Ambiguity

Abstract

As insurers increasingly behave like financial intermediaries and actively participate in capital markets, understanding the dependence structure between insurance and financial risks becomes crucial for insurers' operations. This paper studies dynamic equilibrium insurance pricing when insurers face ambiguity about the correlation between insurance and financial risks and optimally choose underwriting and investment strategies under worst-case beliefs. Correlation ambiguity can generate multiple equilibrium regimes. Contrary to conventional intuition, we find ambiguity does not necessarily increase insurance prices nor reduce insurers' utility.
Paper Structure (16 sections, 9 theorems, 30 equations, 4 figures, 1 table)

This paper contains 16 sections, 9 theorems, 30 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. General Model and Problem Formulation
  3. Insurance Market
  4. Financial Market
  5. Correlation Ambiguity and Optimization Objective
  6. Equilibrium Analysis
  7. Solution to Robust Decision Problem
  8. Case of CARA Utility
  9. Market Equilibrium
  10. Properties of the Equilibrium
  11. Numerical Analysis
  12. Statistical Calibration of Ambiguity Radius
  13. Equilibrium Outcomes under Zero Reference Correlation
  14. Equilibrium Outcomes under Positive Reference Correlation
  15. Equilibrium Outcomes under Negative Reference Correlation
  16. ...and 1 more sections

Key Result

Proposition 1

Assume $\varPi_t$ is compact. Then the value function $V(t, m)$ is the unique deterministic continuous viscosity solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation: with the boundary condition $V(T, m) = u(m)$.

Figures (4)

  • Figure 1: Statistical Calibration of Ambiguity Radius for Different Reference Correlations
  • Figure 2: Equilibrium Outcomes under Zero Reference Correlation
  • Figure 3: Equilibrium Outcomes under Positive Reference Correlation
  • Figure 4: Equilibrium Outcomes under Negative Reference Correlation

Theorems & Definitions (13)

  • Definition 1
  • Remark 1
  • Definition 2
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Theorem 1
  • Remark 2
  • Proposition 4
  • Proposition 5
  • ...and 3 more