Optimal dividend problems for a jump-diffusion  model with capital injections and proportional transaction costs

Chuancun Yin; Kam Chuen Yuen

doi:10.3934/jimo.2015.11.1247

Article Contents

2015, Volume 11, Issue 4: 1247-1262. Doi: 10.3934/jimo.2015.11.1247

This issue Previous Article On EOQ cost models with arbitrary purchase and transportation costs Next Article Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs

Chuancun Yin^1, and
Kam Chuen Yuen^2,

1.
School of Statistics, Qufu Normal University, Shandong 273165
2.
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Received: March 31, 2014

Revised: January 31, 2015

Published: September 2015

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Abstract

In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first problem, we consider the classical dividend problem without capital injections. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of capital injections over strategies with positive surplus at all times. The third problem has the same objective as the second one, but without the constraints on capital injections. Under the assumption of proportional transaction costs, we identify the value function and the optimal strategies for any distribution of gains.

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Mathematics Subject Classification: Primary: 93E20, 91G80; Secondary: 60J75.

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