# 6.9.Kreps

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1. Kreps 2 financial strategies to develop risk load
• Swap Risk-Free Investment for Risky Investment
• Purchase Put Options
2. Kreps 2 constraints when determining risk load
• Safety Constraint: funds available at year end are at least equal to the specified loss safety level (IRR ≥ rf)
• Investment Variance Constraint: variance of reins + inv strategy should be no more volatile than a direct investment in risky assets
3. Kreps Reins + inv compared to equity investment
Writing reinsurance can never really result in dist of capital that are really the same as investment dist because investment returns are strictly limited to having worst-case returns of -100%
4. Kreps Swap Strategy
• (1 + IRR)A = (1 + rf)(P + A) - L
• R = (y - rf)/(1 + rf) * A
• Safety Constraint
• A = (s - μL) / (1 + y)
• s = eμ+ N-1(pct)σ
• σ = √ln(1 + CV²)
• μ = ln(mean) - σ²/2
• Variance Constraint
• A = σLy
5. Kreps Put Option Strategy
• F = (P + A) / (1 + r)
• R = A[(1 + r)(1 + y) - (1 + i)/(1 + i)] + μL[(1 + r)/(1 + i) - 1/(1 + rf)]
• Safety Constraint
• A = 1 / (1 + y) * [(1 + i)/(1 + rf) * s - μL]
• Variance Constraint
• A = [b + √(b² + ac)] / a
• a = σy²(1 + i)² - σi²(1 + y)²
• b = μL(1 + y)σi²
• c = μL²σi² + σL²(1 + i)²

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 Author: Exam9 ID: 68738 Filename: 6.9.Kreps Updated: 2011-02-24 21:27:45 Tags: Kreps Folders: Description: Kreps Show Answers:

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