Upper and lower bounds on dynamic risk indifference prices in incomplete markets

TL;DR

This paper establishes bounds on dynamic risk indifference prices in incomplete markets, showing they are constrained by the dynamic lower and upper hedging prices, thus providing a theoretical framework for pricing under risk measures.

Contribution

It introduces bounds for risk indifference prices in incomplete markets using dynamic convex risk measures, linking them to hedging prices.

Findings

Risk indifference prices are bounded by hedging prices.

Bounds hold in markets with Brownian filtration and finite horizon.

Provides a theoretical basis for pricing in incomplete markets.

Abstract

In the context of an incomplete market with a Brownian filtration and a fixed finite time horizon, this paper proves that for general dynamic convex risk measures, the buyer's and seller's risk indifference prices of a contingent claim are bounded from below and above by the dynamic lower and upper hedging prices, respectively.