Cost-of-capital valuation with risky assets

TL;DR

This paper examines how investing insurance buffer capital in risky assets affects valuation, decomposition, and risk contributions, highlighting the impact of riskiness and limited liability in heavy-tailed risks.

Contribution

It provides a theoretical and numerical analysis of the effects of risky asset investments on cost-of-capital valuation and risk decomposition in insurance.

Findings

Decomposition of buffer capital varies with investment risk level.

Limited liability plays a significant role with heavy-tailed risks.

Explicit results are provided for specific stochastic models.

Abstract

Cost-of-capital valuation is a well-established approach to the valuation of liabilities and is one of the cornerstones of current regulatory frameworks for the insurance industry. Standard cost-of-capital considerations typically rely on the assumption that the required buffer capital is held in risk-less one-year bonds. The aim of this work is to analyze the effects of allowing investments of the buffer capital in risky assets, e.g.~in a combination of stocks and bonds. In particular, we make precise how the decomposition of the buffer capital into contributions from policyholders and investors varies as the degree of riskiness of the investment increases, and highlight the role of limited liability in the case of heavy-tailed insurance risks. We present a combination of general theoretical results, explicit results for certain stochastic models and numerical results that emphasize the key findings.