On Singular Control for Levy Processes

被引：5

作者：

Noba, Kei ^{[1
]}

Yamazaki, Kazutoshi ^{[2
]}

机构：

[1] Inst Stat Math, Sch Stat Thinking, Tokyo 1908562, Japan

[2] Univ Queensland, Sch Math & Phys, Brisbane, Qld 4072, Australia

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2023年 / 48卷 / 03期

基金：

日本学术振兴会;

关键词：

stochastic control; mathematical finance; Levy processes; STOCHASTIC-CONTROL; DIFFUSION DEMANDS; OPTIMAL DIVIDENDS; COMPOUND POISSON; SMOOTH FIT; OPTIMALITY; CONNECTIONS; STRATEGIES; POLICY;

D O I：

10.1287/moor.2022.1298

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We revisit the classical singular control problem of minimizing running and controlling costs. Existing studies have shown the optimality of a barrier strategy when driven by Brownian motion or Levy processes with one-sided jumps. Under the assumption that the running cost function is convex, we show the optimality of a barrier strategy for a general class of Levy processes.

引用

页码：1213 / 1234

页数：22

共 34 条

[1] Russian and American put options under exponential phase-type Levy models [J].

Asmussen, S ;

Avram, F ;

Pistorius, MR .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 109 (01) :79-111

[2] Optimal dividends in the dual model [J].

Avanzi, Benjamin ;

Gerber, Hans U. ;

Shiu, Elias S. W. .

INSURANCE MATHEMATICS & ECONOMICS, 2007, 41 (01) :111-123

[3] On the optimal dividend problem for a spectrally negative Levy process [J].

Avram, Florin ;

Palmowski, Zbigniew ;

Pistorius, Martijn R. .

ANNALS OF APPLIED PROBABILITY, 2007, 17 (01) :156-180

[4] Optimality of doubly reflected Levy processes in singular control [J].

Baurdoux, Erik J. ;

Yamazaki, Kazutoshi .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (07) :2727-2751

[5] Optimizing venture capital investments in a jump diffusion model [J].

Bayraktar, Erhan ;

Egami, Masahiko .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2008, 67 (01) :21-42

[6] ON OPTIMAL DIVIDENDS IN THE DUAL MODEL [J].

Bayraktar, Erhan ;

Kyprianou, Andreas E. ;

Yamazaki, Kazutoshi .

ASTIN BULLETIN, 2013, 43 (03) :359-372

[7]

Benes V. E., 1980, Stochastics, V4, P39, DOI 10.1080/17442508008833156

[8] OPTIMALITY OF AN (s, S) POLICY WITH COMPOUND POISSON AND DIFFUSION DEMANDS: A QUASI-VARIATIONAL INEQUALITIES APPROACH [J].

Benkherouf, Lakdere ;

Bensoussan, Alain .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) :756-762

[9] Optimality of an (s, S) policy with compound poisson and diffusion demands:: A quasi-variational inequalities approach [J].

Bensoussan, A ;

Liu, RH ;

Sethi, SP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 44 (05) :1650-1676

[10]

Bertoin Jean, 1996, Levy processes

← 1 2 3 4 →