Optimal Dividend Strategy In A Jump-Diffusion Model With A Liner Barrier Constraint

For a financial or insurance entity,the problem of finding the optimal dividend distribution strategy and optimal firm value function is a widely discussed topic.Indeed,maximization of the value of a company is common accepted ideas among financial circle.While,the value of the company is always associated with the expected present value of the net dividend payouts since,according to[2],the value of a company in a world of perfect capital markets is exactly the expected present value of future dividends.In the present paper,it is assumed that the firm faces two types of liquidity risks:a Brownian risk and a Poisson risk.The firm can control the time and amount of dividends paid out to shareholders.By sufficiently taking into account the safety of the company,bankruptcy is said to take place at time t if the cash reserve of the firm runs below the linear barrier ktx(10)0(not zero),see[1].We deal with the problem of maximizing the expected total discounted dividends paid out until bankruptcy.The optimal dividend return(or,firm value)function is identified as the classical solution of the associated Hamilton-Jacobi-Bellman(HJB)equation where a second-order differential-integro equation is involved.By solving the corresponding HJB equation,the analytical solution of the optimal firm value function is obtained,the optimal dividend strategy is also characterized,which is of linear barrier type: at time t the firm keeps cash inside when the cash reserves level is less than a critical linear barrier ktx(10)0and pays cash in excess of this linear barrier as dividends.The contents of this article can be divided into five chapters:Chapter 1: sketch the research background of this paper,put forward the target problem,and point out the purposes and significances of this study;Chapter 2: summarize related literatures at home and abroad,outline the research contents and main methods of this thesis;Chapter 3: reformulate the target problem using mathematical models:jump-diffusion model with a liner barrier constraint;Chapter 4: construct the optimal firm value function and the optimal dividend distribution strategy;Chapter 5: conclude the paper,forecast further research;...