# Set-valued risk statistics with the time value of money

## TL;DR

This paper introduces a new class of set-valued risk statistics that incorporate the time value of money, making risk assessment more aligned with financial realities and useful for portfolio risk quantification.

## Contribution

It develops a novel set-valued risk statistic that accounts for the time value of money and provides representation results, enhancing risk analysis in finance and insurance.

## Key findings

- Risk statistics better reflect financial reality.
- New risk measure applicable to portfolio risk.
- Theoretical properties and representations established.

## Abstract

The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In fact, the risk statistics established by this method is closer to financial reality than traditional ones. Moreover, this new risk statistic can be uesd for the quantification of portfolio risk. By further developing the properties related to these risk statistics, we are able to derive representation results for such risk.