Optimal Investment Decision For Insurer With Real Estate And Option Under Different Interest Rates On Deposit And Loan

As one of the important means for insurance companies to maintain and increase the value of their funds and at the same time to improve their ability to resist risks,insurance funds plays an important role in the daily business activities.With the development of the global financial market,the target of insurance investment is becoming more and more abundant,which not only effectively promotes the sustained and healthy development of the global insurance industry,but also deserves attention to the risk problems brought about by the insurance industry.Against this background,Chinese regulators have issued many important departmental regulations to strengthen the normative supervision of the use of insurance funds.In 2010,China issued the interim measures for Insurance companies to invest in real estate,which allows insurance funds to invest in real estate.In 2012,China issued the interim measures on the participation of insurance funds in the trading of financial derivatives,allowing insurance funds to invest in financial derivatives.In addition to the general risk-free securities and real estate,insurance companies can also invest in derivative securities.But the traditional insurance investment literature generally considers risk-free bonds and stocks as investment objects,and the deposit and loan rates considered in the literature are the same,which are inconsistent with the reality.Therefore,under the real market conditions with unequal interest rates on deposit and loan,the in-depth analysis of the real estate investment model restricted by the supervision of our country has important practical significance.Assuming that insurance companies invest in risk-free securities,stocks,real estate and options,the surplus process is a Cramér-lundberg model with pure jumps and the price process of real estate follows the geometric Brownian motion.The depreciation of real estate and its rental income are also considered.Based on the foregoing hypothesis,We first consider the optimal insurance investment decision which includes real estate under the market conditions with unequal interest rates on deposit and loan,then we extend the insurance investment object to options.Finally,the dynamic property of the optimal insurance investment strategy is analyzed by numerical simulation.In model solution,taking exponential function as utility function,the utility maximization model of total asset value of insurance company is established.The model is solved by HJB equation.The process of solving is divided into two steps,the first step is to obtain the optimal investment strategy in different regions by classifying the upper and lower bound constraints of real estate investment.The second step is to obtain the global optimal investment strategy by using the Kuhn-Tucker condition.The results of dynamic analysis in this paper show that,when the initial wealth of the insurance company is fixed,if the yield of the option or real estate is large,the amount of investment in the option or real estate will also be higher.Due to the characteristics of its debt management,insurance companies should construct reasonable portfolios in order to maximize the utility.They also need to hedge the risk effectively by active management and diversified investments.