## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 5, Number 4 (1995), 926-945.

### The Existence of Absolutely Continuous Local Martingale Measures

Freddy Delbaen and Walter Schachermayer

#### Abstract

We investigate the existence of an absolutely continuous martingale measure. For continuous processes we show that the absence of arbitrage for general admissible integrands implies the existence of an absolutely continuous (not necessarily equivalent) local martingale measure. We also rephrase Radon-Nikodym theorems for predictable processes.

#### Article information

**Source**

Ann. Appl. Probab., Volume 5, Number 4 (1995), 926-945.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177004600

**Digital Object Identifier**

doi:10.1214/aoap/1177004600

**Mathematical Reviews number (MathSciNet)**

MR1384360

**Zentralblatt MATH identifier**

0847.90013

**JSTOR**

links.jstor.org

**Subjects**

Primary: 90A09

Secondary: 60G44: Martingales with continuous parameter 46N10: Applications in optimization, convex analysis, mathematical programming, economics 47N10: Applications in optimization, convex analysis, mathematical programming, economics 60H05: Stochastic integrals 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

**Keywords**

Arbitrage immediate arbitrage martingale local martingale equivalent martingale measure representing measure risk neutral measure stochastic integration mathematical finance predictable Radon-Nikodym derivative

#### Citation

Delbaen, Freddy; Schachermayer, Walter. The Existence of Absolutely Continuous Local Martingale Measures. Ann. Appl. Probab. 5 (1995), no. 4, 926--945. doi:10.1214/aoap/1177004600. https://projecteuclid.org/euclid.aoap/1177004600