Extended Reduced-Form Framework for Non-Life Insurance

TL;DR

This paper introduces a flexible continuous-time framework for modeling non-life insurance liabilities, incorporating dependence structures and inflation effects, enabling explicit pricing and hedging in hybrid markets.

Contribution

It generalizes the reduced-form framework to non-life insurance, allowing for dependence between market and insurance information and explicit pricing formulas.

Findings

Provides a unified model for non-life insurance liabilities.

Derives explicit pricing and hedging formulas.

Incorporates inflation and dependence structures.

Abstract

In this paper we propose a general framework for modeling an insurance liability cash flow in continuous time, by generalizing the reduced-form framework for credit risk and life insurance. In particular, we assume a nontrivial dependence structure between the reference filtration and the insurance internal filtration. We apply these results for pricing and hedging non-life insurance liabilities in hybrid financial and insurance markets, while taking into account the role of inflation under the benchmarked risk-minimization approach. This framework offers at the same time a general and flexible structure, and an explicit and treatable pricing-hedging formula.