A multi-dimensional FBSDE with quadratic generator and its applications

Eduard Rotenstein

doi:10.1515/auom-2015-0038

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A multi-dimensional FBSDE with quadratic generator and its applications

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 23 (2015): Issue 2 (June 2015)

By: Eduard Rotenstein

Open Access

|Apr 2017

Abstract

We consider, in the Markovian framework, a multi-dimensional forward - back - ward stochastic differential equation with quadratic growth for the generator function of the backward system. We prove an existence result of the solution and we use this result for pricing and hedging of contingent claims that depend on non-tradeable indexes by portfolios consisting in correlated risky assets.

References

[1] Ankirchner, S; Imkeller, P; Dos Reis, G. - Pricing and hedging of derivatives based on non-tradable underlyings, Mathematical Finance, Vol. 20, No. 2, pp. 289-312 (2010)10.1111/j.1467-9965.2010.00398.x
Search in Google Scholar Back to article
[2] El Karoui, N; Peng, S; Quenez, M.C. - Backward stochastic differential equations in finance, Math. Finance, 7(1), pp. 1-71 (1997)10.1111/1467-9965.00022
Search in Google Scholar Back to article
[3] El Karoui, N.; Rouge, R. - Pricing via utility maximization and entropy, Math. Finance, 10(2), pp. 259-276 (2000)10.1111/1467-9965.00093
Search in Google Scholar Back to article
[4] Hamadène, S.; Hdhiri I. - Backward stochastic differential equations with two distinct reecting barriers and quadratic growth generator, Journal of Applied Mathematics and Stochastic Analysis, Vol. 2006 (Issue 1), pp. 1-28 (2006)10.1155/JAMSA/2006/95818
Search in Google Scholar Back to article
[5] Hamadène, S.; Lepeltier, J.-P.; Peng, S. - BSDEs with continuous coefficients and stochastic differential games, Backward Stochastic Differential Equations, editors N. El. Karoui and L. Mazliak, Longman, Harlow, pp. 115-128 (1997)
Search in Google Scholar Back to article
[6] Imkeller, P; Dos Reis, G; Zhang, J - Results on numerics for FBSDE with drivers of quadratic growth, Contemporary Quantitative Finance (Essays in Honour of Eckhard Platen), pp. 159-182 (2010)10.1007/978-3-642-03479-4_9
Search in Google Scholar Back to article
[7] Kobylanski, M. - Backward Stochastic Differential Equations and Partial Differential Equations with Quadratic Growth, The Annals of Probability, Vol. 28, No. 2, pp. 558-602 (2000)10.1214/aop/1019160253
Search in Google Scholar Back to article
[8] Karatzas, I.; Shreve, S.E. - Brownian motion and Stochastic Calculus, Springer-Verlag, N.Y. (1991)
Search in Google Scholar Back to article
[9] Mania, M; Schweizer, M. - Dynamic exponential utility indifference valuation, Ann. Appl. Probab., 15(3), pp. 2113-2143 (2005)10.1214/105051605000000395
Search in Google Scholar Back to article
[10] Morlais, M.-A. - Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem, Finance Stoch., 13(1), pp. 121-150 (2009)10.1007/s00780-008-0079-3
Search in Google Scholar Back to article
[11] Pardoux, E.; Peng, S. - Solution of a Backward Stochastic Differential Equation, Systems and Control Letters, 14, pp. 55-61, (1990)10.1016/0167-6911(90)90082-6
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2015-0038 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 213 - 222

Submitted on: Dec 1, 2013

Accepted on: Feb 1, 2014

Published on: Apr 22, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Forward-backward SDEs,

Quadratic growth,

Financial derivatives

Related subjects:

Mathematics,

General mathematics

© 2017 Eduard Rotenstein, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 23 (2015): Issue 2 (June 2015)