Risk minimizing of derivatives via dynamic g-expectation and related topics

TL;DR

This paper explores risk minimization strategies for derivatives with non-tradable underlyings using dynamic g-expectations, deriving explicit formulas and analyzing their economic implications in complete markets.

Contribution

It introduces explicit expressions for risk indifference price, marginal risk price, and hedge strategies that are independent of the nonlinear generator g, highlighting market completeness.

Findings

Explicit formulas for risk indifference and marginal risk prices

Optimal strategies derived with initial wealth considerations

Analysis of risk aversion, market price, and economic interpretations

Abstract

In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and [16], we introduce risk indifference price, marginal risk price and derivative hedge and obtain their corresponding explicit expressions. The interesting thing is that their expressions have nothing to do with nonlinear generator g, and one deep reason for this is due to the completeness of financial market. By giving three useful special risk minimization problems, we obtain the explicit optimal strategies with initial wealth involved, demonstrate some qualitative analysis among optimal strategies, risk aversion parameter and market price of risk, together with some economic interpretations.