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Seminar on Stochastic Analysis, Random Fields and Applications VIHedging with Residual Risk: A BSDE Approach

Seminar on Stochastic Analysis, Random Fields and Applications VI: Hedging with Residual Risk: A... [When managing energy or weather related risk often only imperfect hedging instruments are available. In the first part we illustrate problems arising with imperfect hedging by studying a toy model. We consider an airline’s problem with covering income risk due to fluctuating kerosine prices by investing into futures written on heating oil with closely correlated price dynamics. In the second part we outline recent results on exponential utility based cross hedging concepts. They highlight in a generalization of the Black- Scholes delta hedge formula to incomplete markets. Its derivation is based on a purely stochastic approach of utility maximization. It interprets stochastic control problems in the BSDE language, and profits from the power of the stochastic calculus of variations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Seminar on Stochastic Analysis, Random Fields and Applications VIHedging with Residual Risk: A BSDE Approach

Part of the Progress in Probability Book Series (volume 63)
Editors: Dalang, Robert; Dozzi, Marco; Russo, Francesco

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References (13)

Publisher
Springer Basel
Copyright
© Springer Basel AG 2011
ISBN
978-3-0348-0020-4
Pages
311 –325
DOI
10.1007/978-3-0348-0021-1_19
Publisher site
See Chapter on Publisher Site

Abstract

[When managing energy or weather related risk often only imperfect hedging instruments are available. In the first part we illustrate problems arising with imperfect hedging by studying a toy model. We consider an airline’s problem with covering income risk due to fluctuating kerosine prices by investing into futures written on heating oil with closely correlated price dynamics. In the second part we outline recent results on exponential utility based cross hedging concepts. They highlight in a generalization of the Black- Scholes delta hedge formula to incomplete markets. Its derivation is based on a purely stochastic approach of utility maximization. It interprets stochastic control problems in the BSDE language, and profits from the power of the stochastic calculus of variations.]

Published: Feb 4, 2011

Keywords: Financial derivatives; hedging; minimal variance hedging; utilitybased pricing; BSDE; sub-quadratic growth; differentiability; stochastic calculus of variations; Malliavin calculus

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