A functional variational approach to pricing path dependent insurance policies

TL;DR

This paper develops a functional PDE framework using variational methods to accurately price equity-linked insurance policies that depend on the entire historical path of financial assets.

Contribution

It introduces a novel functional PDE approach leveraging functional Itô calculus for pricing path-dependent insurance policies.

Findings

Derivation of a new functional PDE for path-dependent insurance pricing

Application of variational techniques to financial derivatives

Enhanced modeling of policies dependent on asset history

Abstract

The main purpose of this work is the derivation of a functional partial differential equation (FPDE) for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial asset. To this end, we employ variational techniques from the theory of functional It\^o calculus.