Local risk-minimization for Levy markets

被引：10

作者：

Arai, Takuji ^{[1
]}

Suzuki, Ryoichi ^{[2
]}

机构：

[1] Keio Univ, Dept Econ, Minato Ku, 2-15-45 Mita, Tokyo 1088345, Japan

[2] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan

来源：

INTERNATIONAL JOURNAL OF FINANCIAL ENGINEERING | 2015年 / 2卷 / 02期

关键词：

Incomplete markets; local risk-minimization; call options; Asian options; lookback options; Levy processes; Malliavin calculus; Clark-Ocone formula;

D O I：

10.1142/S2424786315500152

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

In this paper, we aim to obtain explicit representations of locally risk-minimizing by using Malliavin calculus for Levy processes. For incomplete market models whose asset price is described by a solution to a stochastic differential equation driven by a Levy process, we derive general formulas of locally risk-minimizing including Malliavin derivatives; and calculate its concrete expressions for call options, Asian options and lookback options.

引用

页数：28

共 17 条

[1] Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics [J].

Barndorff-Nielsen, OE ;

Shephard, N .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2001, 63 :167-207

[2] Explicit representation of the minimal variance portfolio in markets driven by Levy processes [J].

Benth, FE ;

Di Nunno, G ;

Lokka, A ;

Oksendal, B ;

Proske, F .

MATHEMATICAL FINANCE, 2003, 13 (01) :55-72

[3]

Bertoin G., 1998, LEVY PROCESSES

[4]

Choulli T, 1998, ANN PROBAB, V26, P853

[5]

Cont R., 2004, FINANCIAL MODELING J

[6] On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures [J].

Delong, Lukasz ;

Imkeller, Peter .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2010, 120 (09) :1748-1775

[7]

Ishikawa Y., 2013, STOCHASTIC CALCULUS, DOI [10.1515/9783110282009, DOI 10.1515/9783110282009]

[8] Canonical Levy process and Malliavin calculus [J].

Lluis Sole, Josep ;

Utzet, Frederic ;

Vives, Josep .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (02) :165-187

[9]

Protter PE, 2004, STOCHASTIC INTEGRATI, V21

[10]

Sato K, 2013, LEVY PROCESSES INFIN, V68

← 1 2 →