Stability of Utility Maximization in Nonequivalent Markets

TL;DR

This paper investigates the stability of utility maximization in incomplete markets with varying asset volatilities, revealing conditions under which the problem remains stable or becomes unstable.

Contribution

It introduces the first analysis of utility maximization stability in nonequivalent markets with changing volatilities, including a counterexample and positive stability results.

Findings

Expected utility maximization can be unstable in certain nonequivalent markets.

Stability is achieved for utility functions defined on the entire real line.

Counterexamples demonstrate potential degeneracies in market stability.

Abstract

Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of asset prices (as well as the drift) varies. Degeneracies arise from the presence of nonequivalence. In the positive real line utility framework, a counterexample is presented showing that the expected utility maximization problem can be unstable. A positive stability result is proven for utility functions on the entire real line.