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This page provides an intuition for our asset optimisation methodology under SST. The main principles can be applied to both life and non-life insurers’ assets while taking currently held assets as well as liabilities’ market and insurance risk into account.

Optimising Assets under the Swiss Solvency Test

The standard SST model consists of a Delta-Gamma market model, a set of risk bearing capital (RBC) influencing scenarios aggregated with insurance risk (with slightly different aggregation methodologies for life and non-life insurers), credit risk based on the Basel III framework and the market value margin.

 

The basic SST framework

 

  • Different elements of the standard SST framework are affected by the asset or the liability side or by both.
  • We incorporate all elements into our asset optimization framework
sst components

With the elements of the SST model implemented in our systems, we can minimise the target capital ($TC$) under various investment constraints:

\begin{align}
\min_u \quad &TC(u, X_{Mkt}, X_{Scens}, X_{Ins}, Crd) \\
s.t. \quad & Au \leq b\\
& Pu = q
\end{align}
where $u$ are portfolio weights (or more technically unit holdings), $X_{Mkt}$, $X_{Scens}$ and $X_{Ins}$ are stochastic market,
scenario and insurance
risk variables, and $Crd$ is the deterministic Credit Risk. Market and Credit Risk depend both on $u$ while
Insurance risk is independent of assets’ weights. (The market value margin is modelled as a constant not affecting the optimisation results).

While minimising target capital according to the above function is a clearly defined task (even if it is computationally
quite advanced) it typically needs to be constrained according to various considerations. The constraints imposed on the
minimisation function are a set of linear equalities and inequalities with the parameters $A$, $b$, $P$ and $q$ which we group here as follows:

  • Economic risk constraints: setting average portfolio yield to maturity, duration, coupon rate, set predefined weights of specific duration buckets etc.
  • Liquidity constraints: maximum position or issuer size (if an issuer should be excluded the constraint’s value is $0$)
  • Diversification constraints: minimum or maximum allocation to a rating class, sector and region

 

In a nutshell

Our SST asset optimisation method incorporates market, credit and insurance risks of assets and liabilities and minimises SST target capital under various investment constraints (economic risk, diversification and liquidity).