Two Essays on Optimal Asset Allocation with Correlation Risk

Abstract

I investigate optimal strategies of two economic entities considering correlation risk. First topic is problem that optimal asset allocation for investor who consider the correlation risk between stock indices. Second topic is problem that optimal reinsurance and asset allocation for insurer who consider the correlation risk between stock and insurance claim. For both problems, I prove that there exists one and only one solution of my problem and introduce numerical method for solving these problems.

In the first topic, I show that the investor’s optimal investment strategies are non-myopic, and the hedging demand due to correlation risk is significant. When the correlation is low enough, the investor tends to increase the total investment proportion. As a result, investors are exposed to more market risk, leading to a decrease in investor’s utility. Finally, I find that correlation risk is important factor for asset allocation through certainty equivalent wealth analysis.

In the second topic, I derive results that the insurer’s optimal reinsurance and investment strategies are non-myopic, and the hedging demand on account of correlation risk is significantly large. When the correlation is high enough, the insurer decreases reinsurance proportion and increases investment proportion since insurance claim risk could be hedged by stock investment. As a result, insurer exposed to both insurance claim risk and market risk so it has negative effect for the insurer’s utility. In conclusion, I find that correlation risk has significant effect for reinsurance and asset allocation through certainty equivalent wealth analysis.