Hedging of equity-linked with maximal success factor

TL;DR

This paper develops an optimal hedging strategy for equity-linked contracts considering limited capital, market incompleteness, and additional information signals, generalizing previous models to more complex market scenarios.

Contribution

It introduces a new hedging approach maximizing a success factor under market incompleteness and additional information, extending prior models to more general settings.

Findings

Optimal hedging strategy derived for complex market conditions.

Inclusion of nonmarket information signals improves hedging success.

Generalization of existing models to broader market incompleteness.

Abstract

We consider an equity-linked contract whose payoff depends on the lifetime of policy holder and the stock price. We assume the limited capital for hedging and we provide with the best strategy for an insurance company in the meaning of so called succes factor $\IE^\IP\left[{\mathbf 1}_{\{V_T \geq D)}+{\mathbf 1}_{\{V_T < D\}}\frac{V_T}{D}\right ]$, where $V_T$ denotes the end value of strategy and $D$ is the payoff of the contract. The work is a genaralisation of the work of F\"{o}llmer and Schied \cite{FS2004} and Klusik and Palmowski \cite{KluPal}, but it considers much more general "incompletness" of the market, among others midterm nonmarket information signals and infitite nonmarket scenarios.