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RISK-NEUTRAL MEASURES AND PRICING FOR A PURE JUMP PRICE PROCESS

A STOCHASTIC CONTROL APPROACH

Published online by Cambridge University Press:  21 December 2009

Anna Gerardi  and
Paola Tardelli
Anna Gerardi
Affiliation:
Department of Electrical and Information Engineering, University of L’ Aquila, L’ Aquila, Italy E-mail: [email protected]; [email protected]
Paola Tardelli
Affiliation:
Department of Electrical and Information Engineering, University of L’ Aquila, L’ Aquila, Italy E-mail: [email protected]; [email protected]
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Abstract

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process, modeled again by a marked point process. Taking into account the presence of catastrophic events, the possibility of common jump times between the risky asset price process and the arrivals process is allowed. By setting and solving a suitable control problem, the characterization of the minimal entropy martingale measure is obtained. In a particular case, a pricing problem is also discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 1 , January 2010 , pp. 47 - 76
Copyright
Copyright © Cambridge University Press 2009

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