Dynamic risk diversification and insurance premium principles

TL;DR

This paper introduces a dynamic risk valuation method for insurance that accounts for multiple risk diversifications over time, extending classical premium principles with explicit formulas and limit theorems.

Contribution

It develops a novel dynamic valuation framework incorporating multiple risk diversification, extending classical indifference premium principles with explicit formulas and asymptotic results.

Findings

Explicit formulas for dynamic exponential premium principles

Risk loadings decrease to zero with increasing risk divisions

The approach extends classical valuation methods to multi-period settings

Abstract

We present an approach to the dynamic valuation of exposure risks in the multi-period setting, which incorporates a dynamic and multiple diversification of risks in Pareto optimal sense. This approach extends classical indifference premium principles and can be applied for the valuation of insurance risks. In particular, our method produces explicit computation formulas for the dynamic version of the exponential premium principles. Moreover, we show limit theorems asserting that the risk loading for our valuation decreases to zero when the number of divisions of a risk goes to infinity.