On the Existence of Minimax Martingale Measures

Fabio Bellini · Marco Frittelli

183 citations0/0 files storedMathematical Finance

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

Embedding asset pricing in a utility maximization framework leads naturally to the concept of minimax martingale measures. We consider a market model where the price process is assumed to be an d‐semimartingale X and the set of trading strategies consists of all predictable, X‐integrable, d‐valued processes H for which the stochastic integral (H.X) is uniformly bounded from below. When the market is free of arbitrage, we show that a sufficient condition for the existence of the minimax measure is that the utility function u : → is concave and nondecreasing. We also show the equivalence between the no free lunch with vanishing risk condition, the existence of a separating measure, and a properly defined notion of viability.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 183 citations exist upstream.

References

1981Martingales and stochastic integrals in the theory of continuous trading 2008A General Version of the Fundamental Theorem of Asset Pricing (1994)1994A general version of the fundamental theorem of asset pricing 1999The asymptotic elasticity of utility functions and optimal investment in incomplete markets 1991Martingale and Duality Methods for Utility Maximization in an Incomplete Market 1998The fundamental theorem of asset pricing for unbounded stochastic processes 2000The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets 1981Arbitrage and equilibrium in economies with infinitely many commodities

Cited by

2003The minimal entropy martingale measures for geometric L�vy processes 2002The Theory of Good-Deal Pricing in Financial Markets 2002On the optimal portfolio for the exponential utility maximization: remarks to the six‐author paper 2010RISK MEASURES: RATIONALITY AND DIVERSIFICATION 2005ON UTILITY‐BASED PRICING OF CONTINGENT CLAIMS IN INCOMPLETE MARKETS

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.