About the Risk Model of the Optimal Dividend Problems with Stochastic Interest Rate 

Author  YangZuoZuo 
Tutor  ChengJunXiang 
School  Henan Polytechnic University 
Course  Applied Mathematics 
Keywords  Stochastic interest Brownian motion Integraldifferential equation Moment generating function PoissonGeometric process Threshold strategy Barrierstrategy Dividend present value function 
CLC  F224 
Type  Master's thesis 
Year  2012 
Downloads  19 
Quotes  0 
The problem of finding the optimal dividend strategy was first presented by DeFinetti at the15th International Congress of Actuaries in New York City in1957. Atpresent, the study of optimal dividend problems has lasted for more than half a century.For the Brownian motion risk models, we obtain better results. Nowadays, the optimaldividend strategy in a Brownian motion risk model with a constant force of interest wasstudied. But as the market is change, the force of interest is also change with respect tothe time. On these background, this paper discuss the models with stochastic interest.In this thesis, we consider the risk models of dividend payment stochastic interest,in which the surplus process is the Brownian motion process. For the threshold strategy,we obtain integraldifferential equations of the dividend value function and the solutionsof the integraldifferential equations. At the same time, this thesis discuss the dividendpayment about compound PoissonGeometric risk model with stochastic interest, andobtain the integral differential equation satisfied by the value function. In this paperdiscuss the dividend problem of perturbed process with stochastic interest, in which theclaim process is a PoissonGeometric process. And we obtain the integral differentialequations of the dividend present value function, in the exponential claim case, we havethe solution of the integral differential equations. This paper studies a belt stochasticinterest rate risk dependency process, in which the premium income for compoundPoisson process, and claims arise in probability of possibility produced a renewal ofinsurance. By martingale method, the ruin probability satisfy formulas and Lundberginequality is obtained.