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CM2: Financial Engineering & Loss Reserving
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Module 2
Utility Theory and Investment Risk
1
Utility Functions: Non-Satiation & Risk Aversion
Define a utility function and state the conditions for non-satiation and risk aversion.
2
Quantifying Risky Prospects with Expected Utility
Apply the expected utility theorem to rank risky prospects numerically.
3
Risk and Utility: Certainty Equivalent and Risk Premium
Calculate the certainty equivalent and risk premium for a given gamble using power, exponential, and logarithmic utility functions.
4
Quantifying Investment Risk: Variance, Semi-variance, and Shortfall Probability
Calculate variance, semi-variance, and shortfall probability as measures of investment risk.
Calculating VaR
Define and compute Value at Risk (VaR) for given loss distributions.
6
Expected Shortfall: Definition and Calculation
Define and compute Expected Shortfall (Tail VaR / CVaR).
7
VaR vs. Expected Shortfall: Coherence & Sub-additivity
Explain why VaR fails the coherence property of sub-additivity, while Expected Shortfall satisfies it.
Previous module
Foundations of Financial Markets
Next module
Mean-Variance Portfolio Theory