Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

RISK-MINIMIZING HEDGING FOR A SPECIAL CONTINGENTS

  • Published : 2022.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider a risk-minimization hedging problem for a special European contingent claims. The existence and uniqueness of strategy are given constructively. Firstly, a non-standard European contingent is demonstrated as stochastic payment streams. Then the existence of the risk minimization strategy and also the uniqueness are proved under two kinds market information by using Galtchouk-Kunita-Watanabe decomposition and constructing a 0-achieving strategy risk-minimizing strategies in full information. And further, we have proven risk-minimizing strategies exists and is unique under restrict information by constructing a weakly mean-selffinancing strategy.

Keywords

Acknowledgement

This research is supported by Guangxi University of Finance and economics doctoral research start-up project(BS2021024) and National Natural Science Foundation(71271136).

References

  1. H. Follmer, D. Sondermann, Hedging of non-redundant contingent claims, In Mas-Colell A, Hildebrand W Contributions to Mathematical Economics, Amsterdam, North Holland, 1986, 205-223. 
  2. M. Schweizer, Risk-minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994), 327-342.  https://doi.org/10.1111/j.1467-9965.1994.tb00062.x
  3. R. Frey, W.J. Runggaldier, Risk-minimizing hedging stragies under restricted information: The case of stochastic volatility models observable only at discrete random times[J], Mathematical Methods of Operations Research 50 (1999), 339-350.  https://doi.org/10.1007/s001860050101
  4. T. MOller, Risk-minimizing hedging strategies for insurance payment processes, Finance and Stochastics 5 (2001), 419-446.  https://doi.org/10.1007/s007800100041
  5. M. Riesner, Locally risk-minimizing hedging of insurance payment streams, ASTIN Bulletin 37 (2007), 67-92.  https://doi.org/10.2143/AST.37.1.2020799
  6. T.F. Coleman, L. Dmitriy, Y. Li, Discrete hedging of American-type options using local risk minimization, Journal of Banking & Finance 31 (2007), 3398-3419.  https://doi.org/10.1016/j.jbankfin.2007.04.020
  7. B.I. Xiuchun, Zhang Shuguang, Minimizing the Risk of Absolute Ruin Under a Diffusion Approximation Model with Reinsurance and Investment, Journal of Systems Science & Complexity 28 (2015), 144-155.  https://doi.org/10.1007/s11424-015-2084-x
  8. Qian Linyi, Wang Wei, Wang Rong-ming, Risk-minimizing Hedging Strategy for an Equity-indexed Annuity under a Regime Switching Model, Acta Mathematicae Applicatae Sinica 31 (2015), 101-110.  https://doi.org/10.1007/s10255-012-0176-0
  9. N. Vandaeleand, M. Vanmaele, A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Levy process financial market, Insurance: Mathematics and Economics 42 (2008), 1128-1137.  https://doi.org/10.1016/j.insmatheco.2008.03.001
  10. L. Bo, C. Ceci, Locally Risk-minimizing hedging of counterparty risk for portfolio of credit derivatives, Applied Mathematics & Optimization 82 (2020), 799-850.  https://doi.org/10.1007/s00245-018-9549-y
  11. H. Follmer, M. Schweizer, Hedging of contingent claims under incomplete information, In Davis M.H., Elliott R.J. Appllied Stochastic Analysis, Gordon and Breach, London, New York, 1991, 389-414. 
  12. P. Protter, Stochastic Integration and Differential Equations, Springer-Verlag, Berlin, 1990. 
  13. C. Baiocchi and A. Capelo, Variational and Quasi Variational Inequalities, J. Wiley and Sons, New York, 1984. 
  14. D. Chan and J.S. Pang, The generalized quasi variational inequality problems, Math. Oper. Research 7 (1982), 211-222.  https://doi.org/10.1287/moor.7.2.211
  15. C. Belly, Variational and Quasi Variational Inequalities, J. Appl. Math. and Computing 6 (1999), 234-266. 
  16. D. Pang, The generalized quasi variational inequality problems, J. Appl. Math. and Computing 8 (2002), 123-245.