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Modern Actuarial Modelling: Solvency, Aggregate Risks, ALM & Longevity

Reinaldo Marques
Actuarial and Statistics Division - Universitetet i Oslo (sfi)2 - Norwegian Computer Center

Unifal, Brazil, 2013

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Agenda

Solvency, Capital Economic & Aggregate Risks Actuarial Projections, Demographic Risks & Longevity

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Parte I: Solvency, Capital Economic & Aggregate Risks

Basel/ Switzerland

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Source...

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Quantitative Risk Analysis

What is the definition of Risk: future loss of a position-random variable L. And risk measure? mapping from a set of risks to real line L −→ ρ(L) ∈ R+

Examples Insurance risk premium Capital requirement against market risk, credit risk or operat. risk More examples?

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Quantitative Risk Analysis

What is the definition of Risk: future loss of a position-random variable L. And risk measure? mapping from a set of risks to real line L −→ ρ(L) ∈ R+

Examples Insurance risk premium Capital requirement against market risk, credit risk or operat. risk More examples?

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Quantitative Risk Analysis

What is the definition of Risk: future loss of a position-random variable L. And risk measure? mapping from a set of risks to real line L −→ ρ(L) ∈ R+

Examples Insurance risk premium Capital requirement against market risk, credit risk or operat. risk More examples?

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Quantitative Risk Analysis

Axioms for a coherent Measure of Risk L: loss a: ’free of risk’ Translation invariance: ρ(L + a) = ρ(L) + a Positive homogeneity: ρ(L × a) = a × ρ(L) Monotonicity: ρ(L × a) = a × ρ(L) Subadditivity: ρ(L1 + L2 ) ≤ ρ(L1 ) + ρ(L2 ) If we take E[L] as our risk measure...it’s coherent? Check it!

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Quantitative Risk Analysis

Axioms for a coherent Measure of Risk L: loss a: ’free of risk’ Translation invariance: ρ(L + a) = ρ(L) + a Positive homogeneity: ρ(L × a) = a × ρ(L) Monotonicity: ρ(L × a) = a × ρ(L) Subadditivity: ρ(L1 + L2 ) ≤ ρ(L1 ) + ρ(L2 ) If we take E[L] as our risk measure...it’s coherent? Check it!

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