# Solvency Analytics News

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

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).