Based
on utility theory, this paper firstly combined different utility functions with
risk aversion coefficient and constructed different kinds of optimizing problems for hedgers to hedge for
stochastic-payment-typed contingent claim, and then, by the aid of
dynamic programming theory, effective multi-stage hedging strategy is proposed
for different risk-averse hedgers. Lastly, the research results that the
optimal hedging ratios for three kinds of utility functions are equivalent and
do not relate to the risk aversion coefficient.
References
[1]
Bouleau, N. and Lamberton, D. (1989) Residual Risks and Hedging Strategies in Markovian Markets. Stochastic Processes and their Applications, 33, 131-150.
https://doi.org/10.1016/0304-4149(89)90071-9
[2]
Cerny, A. (2004) Dynamic Programming and Mean-Variance hedging in Discrete Time. Applied Mathematical Finance, 11, 1-25.
https://doi.org/10.1080/1350486042000196164
[3]
Gugushvili, S. (2003) Dynamic Programming and Mean-Variance Hedging in Discrete Time. Georgian Mathematical Journal, 10, 237-246.
[4]
Duffie, D. and Richardson, H.R. (1991) Mean-Variance Hedging in Continuous Time. The Annals of Probability, 1, 1-15. https://doi.org/10.1214/aoap/1177005978
[5]
Laurent, J.P. and Pham, H. (1999) Dynamic Programming and Mean-Variance Hedging. Finance Stochast, 3, 83-110.
[6]
Yang, J.Q. and Xiao, Q.X. (2010) Risk-Minimizing Hedging for Contingent Claims with Stochastic Payments. Applied Mathematics a Journal of Chinese Universities, 25, 1-8.
[7]
Zhang, W., Zhou, D. and Liu, L. (2013) Contracts for Changing Times: Sourcing with Raw Material Price Volatility and Information Asymmetry. Manufacturing & Service Operations Management, 16, 133-148.
https://doi.org/10.1287/msom.2013.0454
[8]
Ni, J., Chu, L.K., Wu, F., et al. (2012) A Multi-Stage Financial Hedging Approach for the Procurement of Manufacturing Materials. European Journal of Operational Research, 221, 424-431. https://doi.org/10.1016/j.ejor.2012.03.031
[9]
Arrow, K.J. (1971) The Theory of Risk Aversion. Essays in the Theory of Risk-Bearing, 90-120.
[10]
Li, Y.H., Wei, Y. and Chen, W. (2014) Application of Risk Aversion to Stock Index Futures Hedging. Journal of Industrial Engineering/Engineering Management, 4, 173-179.
[11]
Yao, H.X. and Li, Z.F. (2014) Expected Utility Maximization Optimal Portfolio Selection Based on Non-parametric Estimation Framework. Chinese Journal of Management Science, 22, 1-9.
[12]
Lewis, F.L. and Syrmos, V.L. (1995) Optimal Control. 2nd Edition, John Wiley & Sons, New York, 315.
