Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

An integral representation theorem of g-expectations

An integral representation theorem of g-expectations There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (Ann. Inst. Fourier (Grenoble) 5 (1955), 131–295), the other is the Peng's g-expectation given by Peng (BSDE and Related g-Expectation, Longman, Harlow, 1997, pp. 141–159) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations under which Peng's g-expectation can be represented by a Choquet expectation for some random variables (Markov processes). It is well known that Choquet expectation and g-expectation (also BSDE) have been used extensively in the pricing of options in finance and insurance. Our result also addresses the following open question: given a BSDE (g-expectation), is there a Choquet expectation operator such that both BSDE pricing and Choquet pricing coincide for all European options? Furthermore, the famous Feynman–Kac formula shows that the solutions of a class of (linear) partial differential equations (PDE) can be represented by (linear) mathematical expectations. As an application of our result, we obtain a necessary and sufficient condition under which the solutions of a class of nonlinear PDE can be represented by nonlinear Choquet expectations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Risk and Decision Analysis iospress

An integral representation theorem of g-expectations

Risk and Decision Analysis , Volume 2 (4) – Jan 1, 2011

Loading next page...
 
/lp/iospress/an-integral-representation-theorem-of-g-expectations-dvBIQWhb7l
Publisher
IOS Press
Copyright
Copyright © 2011 by IOS Press, Inc
ISSN
1569-7371
eISSN
1875-9173
DOI
10.3233/RDA-2011-0047
Publisher site
See Article on Publisher Site

Abstract

There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (Ann. Inst. Fourier (Grenoble) 5 (1955), 131–295), the other is the Peng's g-expectation given by Peng (BSDE and Related g-Expectation, Longman, Harlow, 1997, pp. 141–159) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations under which Peng's g-expectation can be represented by a Choquet expectation for some random variables (Markov processes). It is well known that Choquet expectation and g-expectation (also BSDE) have been used extensively in the pricing of options in finance and insurance. Our result also addresses the following open question: given a BSDE (g-expectation), is there a Choquet expectation operator such that both BSDE pricing and Choquet pricing coincide for all European options? Furthermore, the famous Feynman–Kac formula shows that the solutions of a class of (linear) partial differential equations (PDE) can be represented by (linear) mathematical expectations. As an application of our result, we obtain a necessary and sufficient condition under which the solutions of a class of nonlinear PDE can be represented by nonlinear Choquet expectations.

Journal

Risk and Decision Analysisiospress

Published: Jan 1, 2011

There are no references for this article.