Optimal Dividend and Investing Control of a Insurance Company with Higher Solvency Constraints 

Author  HuangJianPing 
Tutor  LiangZongXia 
School  Tsinghua University 
Course  Mathematics 
Keywords  Solvency Suboptimal control strategy Suboptimal return function The probability of bankruptcy Stochastic Differential Equations 
CLC  F840 
Type  Master's thesis 
Year  2010 
Downloads  89 
Quotes  0 
This article discusses the optimal control problem of the large insurance companies, the management of the company through dividend distribution process, the means to achieve the purpose of the company to invest in the financial markets and reinsurance to control exposure. The company will set a minimum asset limit m GT; 0, the company must make its own assets has been greater than m, once the asset is less than or equal to m, were identified as bankruptcy. We assume that insurance companies can only be proportional reinsurance to reduce their risk exposure, the first goal of the optimization problem is to find an optimal control strategy pi ^{ including reinsurance ratio and dividend payment plans * = {a pi * (t), L t pi * }, so that shareholders before the company went bankrupt cumulative return. The second goal of the optimization problem is to make the insurance company to meet the requirements of security, insurance is a need to consider the business of the public interest, must be considered in order to protect the interests of policy holders adequate solvency. Solvency constraints give the choice of strategy additional restrictions may make insurance strategy can not be executed to maximize revenue, the decrease in the return to shareholders, the two goals are usually not at the same time to achieve the best. The purpose of this paper is to seek to maximize revenue and improve seek an optimal balance between security, to solve the optimal control problem of the large insurance companies under higher solvency and security. By controlling the minimum dividends sector b solvency limit, and obtain the lowest Dividend Barrier b suboptimal return function V (x, b) and the corresponding suboptimal control strategy pi b * . Solvency is defined as the requirements of the initial assets does not exceed the probability of bankruptcy in finite time T b insurance companies epsilon gt; 0, the P [the τ b pi b * ≤ T] ≤ ε. The main goal of this paper is that from B: = b: P [τ b b ≤ T] ≤ epsilon find a b the * ∈ B, V (x, b * ) = sup b ∈ B {V (x, b)}. To achieve this goal, we will show that P [τ b π b * ≤ T] b continuous monotonically decreasing when the nature of the b → 0 tends to zero, and come to the suboptimal return function V (x, b) the nature of the b monotonous lowdown. Therefore b * = minB, making the V (b * ) = the sup b ∈ B {V (x, b)}. The main innovation lies in the discussion of the bankruptcy sector m, proved m gt; the 0 is bankruptcy probability the P [τ , b pi b * ≤ T] is strictly greater than zero lower bound, thus proving the discussion on the limitations of the solvency meaningful. }