The Research Of Asset-liability Model Under Jump-diffusion Process

Portfolio is an important research topic that has received a great deal of attentionin financial investment theory, and is also an important research area of modernfinancial engineering. More specially, asset-liability management, as one of importantresearch fields in modern portfolio management and risk management, has drawn anincreasing attention.In1990，Sharpe and Tint[11]added liability to portfolio management for the firsttime, and studied a mean-variance portfolio selection model under the condition ofliability, then established a theoretical foundation for further analysis of asset-liabilitymanagement. In2008, Xie et al.[18]constructed a continuous-time mean-varianceportfolio selection model with multiple risky assets and one liability in an incompletemarket, thus derived the optimal portfolio strategy and the efficient solution ofmean-variance model.Based on the above work, we consider asset-liability management portfolioproblem with jump-diffusion process, and add a jump part into the existing assetmodels in this work.In contrast to the research of Xie et al., we assume portfolio selection under thebackground of an incomplete market, and use a method of dimensionality reduction tocreate a complete market. We introduce a jump part into the asset models, which has acorrelative relationship with liability. We use dynamic programming in stochasticcontrol theory and HJB equation, thus get the optimal investment proportion andexpected investment income, which meet the objective function. That is，we get ananalytic expression of the optimal investment strategy and the portfolio expectedinvestment income in asset-liability model with jump-diffusion process. Also, westudy the risk management and the optimal portfolio problem under asset-liabilitymodel of different interest rates with jump-diffusion process. In this paper, theresearch can be regarded as a natural extension of asset-liability management.