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Stochastic Dominance

How do I decide whether an investment is

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Stochastic Dominance

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    1. Stochastic Dominance A Tool for Evaluating Reinsurance Alternatives

    2. How do I decide whether an investment is “profitable”. Is return commensurate with “risk”? Does investment diversify my portfolio or concentrate exposure? Is investment consistent with my preferred operating risk?

    3. Common Measures of Risk and Reward Internal Rate of Return Return on Equity Net Present Value Loss Ratio Return on Capital Expected Policyholder Deficit

    4. Problems with these measures... Blow up in real life. Can’t compare investments of different size. “Show me the capital!” Don’t consider portfolio-level impact.

    5. What to do then? Utility Theory (Please suppress groans) Basic premise is “Tell me how much a return of W is worth to you...” “…then we can see if the investment improves your expected worth.”

    6. Review of Utility Theory A utility function is a transformation that maps dollars to utility (worth). The shape of this function reflects our investment objectives and preferred operating risks. Common features include Wealth Preference and Risk Aversion

    7. Wealth Preference “Greed is good.” A utility function U(w) possesses Wealth Preference if and only if U’(w)ł 0 for all w with at least one strict inequality. In other words, my utility function is increasing (there are a lot of ways to be increasing, though).

    8. Risk Aversion I hate losing more than I like winning. A utility function U(w) possesses Risk Aversion if and only if it satisfies Wealth Preference and U’’(w)Ł 0 for all w with at least one strict inequality. In other words, my utility function is increasing at a decreasing rate (i.e. it’s curved).

    9. A Less Common Feature: Ruin Aversion Also called Decreasing Absolute Risk Aversion, Skewness Preference, etc. Losing a little is bad, but losing everything is intolerable. Enter reinsurance...

    10. Ruin Aversion A utility function U(w) possesses Ruin Aversion if and only if it satisfies Risk Aversion and U’’’(w)ł 0 for all w with at least one strict inequality. In other words, my utility is curved but “flattening out” as it goes.

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