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