Abstract
This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment. Spectral risk measure could describe the degree of risk aversion, so the underlying strategy might take the investor's risk attitude into account. We establish an optimization model aiming at maximizing risk-adjusted return of capital (RAROC) involved with spectral risk measure. The theoretical result is derived and empirical study is displayed under different risk measures and different confidence levels comparatively. The result shows that risk attitude has a significant impact on investment strategy. With the increase of risk aversion factor, the investment ratio of risk asset correspondingly reduces. When the aversive level increases to a certain extent, the impact on investment strategies disappears because of the marginal effect of risk aversion. In the case of VaR and CVaR without regard for risk aversion, the investment ratio of risk asset is increasing significantly.
Highlights
Underwriting business and investment business are two main fund sources of an insurance company
This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment
The result tells us that more risk aversion will decrease the investment ratio in risk asset and increase the interest of investing in risk-free asset
Summary
Underwriting business and investment business are two main fund sources of an insurance company. The relationship between return and risk needs to be fully balanced in insurance investment, in which mean-risk optimization is the most commonly used criterion. For example, Lambert and Hofflander [1], Kahane and Nye [2], and Briys [3], established optimal portfolio model for property insurance under mean-variance criterion. Ruin probability and some down-side risk measures such as VaR and CaR were introduced into insurance business to find the optimal investment strategy. To the best of our knowledge, there is no literature which studied optimal investment problem in insurance business based on SRM. This paper will introduce spectral risk measure into optimal investment model with RAROC as optimization target, construct optimization model, and give its theoretical and empirical study.
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