Optimal Investment For An Insurer With Multiple Risky Assets In An Incomplete Market

Economic globalization makes the insurance industry more competitive．Besidesmaking efforts to develop new types of insurance products，improving the servicelevel of the insurance，the insurance fund investment income has gradually becomethe important way to increase the profit of insurance company，which affects itsmarket competition ability．In order to adapt to the fierce competition in the market，our country insurance funds utilization is gradually catching up with the worldcommunity at present．The proportion invested in bank deposits，government bonds isdeclining，as well as the proportion invested in risk assets such as the financial bonds，corporate bond，securities investment funds and stocks is on a rising trend．Therefore，the insurance fund investment has become a significant content in the field ofactuarial science．Nowadays，research on portfolio and derivatives pricing by the means of thestochastic control theory has great progress，which has been applied in insuranceinvestment research gradually．Based on the analysis of previous studies，this paperconsidered a more general risk model: in the incomplete market，the claim process isassumed to follow a Brownian motion with drift．The insurance company is allowedto invest in a risk-free asset and multiple risky assets; the claim process is related tothe risky asset processes．The assumptions above make the research more realistic．First of all，considering the optimal proportional reinsurance，the optimalinvestment strategy of maximizing the expected utility of terminal wealth isinvestigated and the HJB equation of this problem is also established．For exponentialutility function，the explicit expressions for the optimal investment and reinsurancestrategies are obtained．Then in the special case that there is no proportionalreinsurance，the equivalent relation of the optimal strategies of maximizing theexpected exponential utility of terminal wealth and minimizing the probability of ruinis discussed in detail．Finally，the influence of the relation between claim process andrisky asset processes on the optimal investment strategy is analyzed emphatically．Theconclusions suggest that the insurer should choose the risky asset that has a negativecorrelation coefficient with claims process to invest．The conclusion is of greattheoretical and practical significance for insurance company to select the best assets toinvest in．...