Entropic Conditions and Hedging

Samuel Njoh

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 197-216
  • ISSN: 1292-8100

Abstract

top
In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential utilities when the risk premium is bounded. Our result is based upon backward stochastic differential equation (BSDE) and a good choice of admissible strategies which allows us to solve our hedging problem.

How to cite

top

Njoh, Samuel. "Entropic Conditions and Hedging." ESAIM: Probability and Statistics 11 (2007): 197-216. <http://eudml.org/doc/250121>.

@article{Njoh2007,
abstract = { In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential utilities when the risk premium is bounded. Our result is based upon backward stochastic differential equation (BSDE) and a good choice of admissible strategies which allows us to solve our hedging problem. },
author = {Njoh, Samuel},
journal = {ESAIM: Probability and Statistics},
keywords = {Stochastic optimization; martingale representation theorem.; stochastic optimization; martingale representation theorem},
language = {eng},
month = {6},
pages = {197-216},
publisher = {EDP Sciences},
title = {Entropic Conditions and Hedging},
url = {http://eudml.org/doc/250121},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Njoh, Samuel
TI - Entropic Conditions and Hedging
JO - ESAIM: Probability and Statistics
DA - 2007/6//
PB - EDP Sciences
VL - 11
SP - 197
EP - 216
AB - In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential utilities when the risk premium is bounded. Our result is based upon backward stochastic differential equation (BSDE) and a good choice of admissible strategies which allows us to solve our hedging problem.
LA - eng
KW - Stochastic optimization; martingale representation theorem.; stochastic optimization; martingale representation theorem
UR - http://eudml.org/doc/250121
ER -

References

top
  1. D. Becherer, Rational Hedging and Valuation with Utility-Based Preference. PhD Thesis, Berlin University (2001).  
  2. D. Becherer, Rational Hedging and Valuation of Integrated Risks under Constant Absolute Risk Aversion, Insurance: Math. Econ. 33 (2003) 1–28.  Zbl1072.91025
  3. J. Cvitanic, W. Schachermayer and H. Wang, Utility Maximization in Incomplete Market with Random Endowment, in Proceedings of Symposia in Applied Mathematics (1999).  Zbl0993.91018
  4. M. Davis, Optimal Hedging with Basis Risk, preprint (2000).  Zbl0992.91045
  5. M. Davis, Option Valuation and Hedging with Basis Risk, in System Theory: Modeling, Analysis and Control, T.E. Djaferis and I.C. Schick Eds., Kluwer, Amsterdam (1999).  
  6. F. Delbaen and W. Schachermayer, Arbitrage and Free Lunch with Bounded Risk for Unbounded Continuous Processes, Mathematical Finance4 (1994) 343–348.  Zbl0884.90024
  7. F. Delbaen, P. Grandits, T. Rheinlander, D. Samperi, M. Schweizer and C. Stricker, Exponential Hedging and Entropic Penalties. Mathematical Finance12 (2002) 99–123.  Zbl1072.91019
  8. N. El Karoui and R. Rouge, Pricing via Utility Maximization and Entropy, Mathematical Finance10 (2000) 259–276.  Zbl1052.91512
  9. W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control. Springer Verlag, New York (1975).  
  10. V. Henderson, Valuation of Claims of Non Traded Assets using Utility Maximization, Mathematical Finance12 (2002) 351–373.  Zbl1049.91072
  11. Y.M. Kabanov and C. Stricker, On the Optimal Portfolio for the Exponential Utility Maximization: Remarks to the Six-Author Paper, Mathematical Finance12 (2002) 125–134.  Zbl1073.91034
  12. I. Karatzas and S.E. Shreve, Methods of Mathematical Finance. Springer Verlag, New York (1998).  Zbl0941.91032
  13. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus. Springer Verlag (1991).  Zbl0734.60060
  14. M. Kobylanski, Backward Stochastic Differential Equations and Partial Differential Equations with Quadratic Growth, The Annals of Probability2 (2000) 558–602.  Zbl1044.60045
  15. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Springer Verlag (1991).  Zbl0731.60002
  16. W. Schachermayer, Optimal Investment in an Incomplete Market, in H. Geman et al. Eds. Mathematical Finance Bachelier Congress (2000), Berlin Heidelberg New York, Springer (2002).  
  17. M. Yor. Sous-Espaces Denses dans L1 ou H1, in Séminaire de Probabilités XII, Springer Verlag (1978) 265–309.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.