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**and security of benefits in occupational pension institutions (IORPS) **

Speaker(s): Stefan Nellshen (Bayer-Pensionskasse VVaG)

We assess how certain regulatory requirements for occupational pension institutions (IORPs) influence (asset-liability-management-based) investment behavior and the long-term-probability Ψ that the guaranteed benefits can always be paid, when due. We assume an investment universe of nϵIN asset classes. An investment strategy is a (z1,…,zn)ϵIRn with zi = relative weight of the i-th asset class. We assume z1+…+zn=1 and zi≥0 for all i. Let the random returns of each asset class in different periods be stochastically independent but having the same probability distribution. Let ρ be any continuous convex risk measure. Using topological arguments we show: if the asset class offering the highest expected return has the highest risk, then the "generalized efficient frontier" in (ρ,μ)-coordinates (μ = return expectation of the respective investment strategy) exists over a connected area of the ρ-axis, is continuous in ρ, monotonically increasing and concave. This is a generalization of ordinary capital market theory.

Increasing maximum quotas for single asset classes increases Ψ. Hence, maximum quotas (if used at all) should be relatively high just in order to hinder any unreasonable behavior.

Let φ denote the probability, that the IORP always fulfils its regulatory funding requirements. We assume that φ and Ψ depend on μ and ρ (inter alia) and: ρ1 < ρ2 => φμ, ρ1≥φμ, ρ2 and μ1>μ2 => φ μ1, ρ ≥ φ μ2, ρ ; analogously for Ψ. The problem is: an IORP trying to maximize φ (or to keep φ at a certain minimum level), does not automatically optimize Ψ (what it should do!). Mathematical criteria are developed, under which circumstances an easing of regulatory funding requirements can improve Ψ, and if the resulting investment strategy will be more or less risky. We sketch, what this means for Solvency II. Several practical applications are presented, e.g. for a low interest environment.

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