Research On Investment-Liabilities Management With Transaction Costs

The financial tsunami lasted for years has brought an unparalleledcatastrophe to the world economy. Many world-famous financial institutions, such asCitibank, Lehman Brothers and other corporations with high level of management didnot survive, but all suffered huge loss and even bankruptcy. The financial crisis wakesup the financial field and make investors to attach more importance to issues such asrisk prevention and risk management.As an important part of modern financial management, asset-liabilitymanagement has draw the attention of more and more scholars. Moreover, lots offinancial organizations, both from home and abroad, regard it as a symbol to enhancethe key competitiveness. This article will study asset-liability management incontinuous time framework, and discuss optimal investment strategies withlogarithmic utility function.This article study portfolio investment that stochastic interest rates andliabilities are considered, study the optimal portfolio investment strategy with theliabilities. This article assumes that interest rates follow the random process of theVasicek model, and assumes that the interest rate process, the stock price process, andliabilities were related, and establishes optimal models for portfolio investment tomeet the expected utility of terminal wealth maximization. HJB equation is achievedthrough the maximum principle, and studies the logarithmic utility function and theoptimal investment strategy. Also, asset-liability management analytical expressionis achieved by solving the corresponding partial differential equation under the utilityfunction. Illustrations are given to enhance the operability of the research, which is ofguiding significance.This article firstly describes the research background, research status both athome and abroad, problems and main research achievements of portfolio investmentand portfolio investment liabilities. Then, it introduces the discrete-timecontinuous-time portfolio investment and portfolio investment research, as well asutility functions. Finally, the article studies the investment portfolio with the liabilities,and analyzes it with practical cases.