分数Black-Scholes市场中的动态下跌风险

Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (6): 1674-1682.

• Articles • Previous Articles Next Articles

Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market

ZHANG Hua-Yue¹, CHEN Wan-Hua², QU Li-An³

1.Department of Finance, School of Economics, Nankai University, Tianjin 300071;
2.DeGroote School of Business, |McMaster University, L8S 4L8;
3.Peking University, Beijing 100083

Received:2008-04-10 Revised:2011-07-12 Online:2011-12-25 Published:2011-12-25
Supported by:
国家自然科学基金(10901086)和国家重点基础研究发展计划(973计划) (2007CB814905)资助

Abstract

Abstract:

The paper is concerned with continuous time portfolio selection model in a complete Black-Scholes market driven by fractional Brownian motion with Hurst parameter H>1/2. The objective is to find an admissible portfolio π to minimize the risk measured by below target semi-variance. By the martingale method in Cox and Huang, we derive the optimal terminal wealth and the corresponding optimal investment strategy. Finally, we numerically analyze the properties of Downside risk measure, the result shows that Hurst index H must not be lost sight.

Key words: Downside risk, Fractional Brownian motion, BTSV, Clark-Ocone theorem, Lagrange multiplier

CLC Number:

60G15

ZHANG Hua-Yue, CHEN Wan-Hua, QU Li-An. Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market[J].Acta mathematica scientia,Series A, 2011, 31(6): 1674-1682.

Trendmd

References

[1] Cox J C, Huang C. Optimal consumptions and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory, 1989, 49: 33--83

[2] Markowitz H. Portfolio selection. Journal of Finance, 1952, 7: 77--91

[3] Markowitz H. Portfolio Selection. New York: John Wiley And Sons, 1959

[4] Nawrocki D N. A brief history of downside-risk measures. The Journal of Investing, 1999, 8: 9--25

[5] Fishburn P. Mean-risk analysis with risk associated with below-target returns. Amer Econ Rev, 1977, 67: 116--125

[6] Hu Y Z, Øksendal B, Sulem A. Optimal Portfolio in Fractional Black-Scholes Market//Albeverio S, et al (Ed.). Mathematical Physics and Stochastic Analysis. Singspore: World Scientific, 2000a: 267--279

[7] Biagini F, Hu Y Z, {\O}ksendal B, Sulem A. A stochastic maximum principle for processes driven by fractional Brownian motion. Stochastic Process and Application, 2002, 100: 233--253

[8] Hu Y Z, Øksendal B, Sulem A. Optimal consumption and portfolio in a Black-Scholes market driven by fractional Brownian motion. Infin Dimens Anal Quantum Probab Relat Top, 2003, 6: 519--536

[9] Hu Y Z, {\O}ksendal B, Sulem A. Fractional white noise calculus and applications to finance. Infin Dimens Anal Quantum Probab Relat Top, 2003, 6: 1--32

[10] Manderlbort B, van Ness J. Fractional brownian motions, fractional noise and applications. SIAM Review, 1968, 10: 422--437

[11] Duncan T E, Hu Y Z, Pasik-Duncan B. Stochastic calculus for fractional Brownian motion. SIAM Journal on Control and Optimization, 2000, 38: 582--612

[12] Norros I, Valkeila E, Virtamo J. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, 1999, 5(4): 571--587

Dynamic Below-Target Semi-Variance Risk Measure in a Fractional |Black-Scholes Market

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 2

Metrics

Comments

Recommended 10

[1]	Liu Shaoyue; Yang Xiangqun. Optimal Portfolio in a Fractional Black-Scholes Model with Arbitrary Hurst Parameter [J]. Acta mathematica scientia,Series A, 2008, 28(4): 742-746.
[2]	CHEN Ye-Hua, CHEN Zhen-Long. The Maximum Entropy Function Sequence for Convex Programming and Its Convergence [J]. Acta mathematica scientia,Series A, 2004, 4(6): 767-771.