**diversification** - putting resources into different risky situations

- can't lose on all investments
- invesments not too closely correlated >> eliminates some risk
- negatively correlated - good results for 1 investment means bad results for another investment
- positively correlated - investments moving in the same direction, in response to economic changes

**insurance** - uses risk premiums

- insurance cost = expected loss
- law of large numbers - aility to avoid risk by operating on a large scale
- if insurance premium = expected payout, then
**actuarially fair**- insurance companies need to profit >> charge more than expected losses

Dan has a wealth utility function of U = lnw. He currently has $1200, but there's a 1/8 chance that his car will blow up and he'll lose $1000. However, he could pay insurance 30 cents on the dollar to cover his potential losses. How much insurance should he pay?

- you want to maximize expected utility
- x = amount he covers w/ insurance
- he'll pay 0.3x for the insurance

- if his car doesn't blow up, he'll have w = 1200 - 0.3x
- if his car does blow up, he'll have w = (1200-1000) - 0.3x + x
- gets back the x amount he covers
- be sure to include the 0.3x amount that he still paid

- EU = (7/8) ln(1200 - 0.3x) + (1/8) ln(200 + 0.7x)
- d(EU)/dx = 0 = (-2.1/8) / (1200 - 0.3x) + (0.7/8) / (200 + 0.7x)
- (2.1/8) / (1200 - 0.3x) = (0.7/8) / (200 + 0.7x)
- 2.1 / (1200 - 0.3x) = 0.7 / (200 + 0.7x)
- 420 + 1.47x = 840 - 0.21x
- 1.68x = 420
- x = $250

**value of complete information** - difference between expected value of choice w/ and w/o complete information

- calculates how much firm would pay for extra information/predictions for sales
- also dependent on whether firm is risk averse/neutral/loving