Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
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Some Results from Arbitrage Opportunity on Nonlinear Wealth Processes
Thoednithi Kirati
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2015 Volume 28 Issue 7 Pages 291-298

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Abstract

In this paper, we mainly concern about nonlinear BSDE which is often used to describe a case of constraint on the wealth of an investor. Unlike the linear case, we can show that under a certain situation, both buyer and seller can create arbitrage opportunities in the derivative market. We utilize a relation between BSDE and PDE in order to obtain the bounds of a solution. As a result, we succeed in establishing a sufficient condition which guarantees the existence of the arbitrage opportunities, and the limitation of the arbitrages as well. In addition, we are able to extend the results to a more general class of models and accomplish in strengthening the comonotonic theorem for BSDEs. Furthermore, by applying the results, we obtain a sufficient condition that ensures the additivity of g-expectation even when a generator of BSDE is nonlinear.

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© 2015 The Institute of Systems, Control and Information Engineers
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