Continuity of utility maximization under weak convergence

被引：9

作者：

Bayraktar, Erhan ^{[1
]}

Dolinsky, Yan ^{[2
]}

Guo, Jia ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Hebrew Univ Jerusalem, Dept Stat, Jerusalem, Israel

来源：

MATHEMATICS AND FINANCIAL ECONOMICS | 2020年 / 14卷 / 04期

基金：

美国国家科学基金会;

关键词：

Incomplete markets; Utility maximization; Weak convergence; STOCHASTIC VOLATILITY; OPTIMAL CONSUMPTION; PORTFOLIO POLICIES; SUPER-REPLICATION; MARTINGALE; STABILITY; DISCRETE; OPTIONS; PRICES; SPACE;

D O I：

10.1007/s11579-020-00274-x

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence result for the terminal wealths of the optimal portfolios. Finally, we apply our results to the computation of the minimal expected shortfall (shortfall risk) in the Heston model by building an appropriate lattice approximation.

引用

页码：725 / 757

页数：33

共 43 条

[1]

[Anonymous], 2001, Finance and Stochastics, DOI DOI 10.1007/PL00013534

[2]

[Anonymous], 1992, Math. Finance, DOI [DOI 10.1111/J.1467-9965.1992.TB00022.X, DOI 10.1111/j.1467-9965.1992.tb00022.x]

[3] Hedging and portfolio optimization in financial markets with a large trader [J].

Bank, P ;

Baum, D .

MATHEMATICAL FINANCE, 2004, 14 (01) :1-18

[4] Stability of exponential utility maximization with respect to market perturbations [J].

Bayraktar, Erhan ;

Kravitz, Ross .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (05) :1671-1690

[5] A unified framework for utility maximization problems: An Orlicz space approach [J].

Biagini, Sara ;

Frittelli, Marco .

ANNALS OF APPLIED PROBABILITY, 2008, 18 (03) :929-966

[6]

Billingsley P., 1968, CONVERGE PROBAB MEAS

[7] Bootstrap random walks [J].

Collevecchio, Andrea ;

Hamza, Kais ;

Shi, Meng .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2016, 126 (06) :1744-1760

[8] OPTIMAL CONSUMPTION AND PORTFOLIO POLICIES WHEN ASSET PRICES FOLLOW A DIFFUSION PROCESS [J].

COX, JC ;

HUANG, CF .

JOURNAL OF ECONOMIC THEORY, 1989, 49 (01) :33-83

[9] A THEORY OF THE TERM STRUCTURE OF INTEREST-RATES [J].

COX, JC ;

INGERSOLL, JE ;

ROSS, SA .

ECONOMETRICA, 1985, 53 (02) :385-407

[10] Super-replication in stochastic volatility models under portfolio constraints [J].

Cvitanic, J ;

Pham, H ;

Touzi, N .

JOURNAL OF APPLIED PROBABILITY, 1999, 36 (02) :523-545

← 1 2 3 4 5 →