Mean Variance Optimization of Non-Linear Systems and Worst-case Analysis



is the total expected cost of refinancing, and the last one is the total expected repayment
to depositors. The operation of the internal money market can be seen in the third term of
(11), where the total demand for liquidity,
xm = δ1D1 + δ2D2, and reserves, Rm = R1 + R2,
are pooled together.

A preliminary step before deriving the optimal reserve-deposit ratio of the merged banks
is to understand their ‘deposit market policy’. Whether they raise equal or different amounts
in both regions affects the distribution of the demand for liquidity
xm , and thus the size of
the expected cost of refinancing. We have the following lemma.

Lemma 1 The merged banks raise an equal amount of deposits in each region, i.e., D1 =
D2 = Dm.

Lemma 1 shows that the merged banks not only raise deposits in both regions, but they
even do it symmetrically. Choosing equal amounts of deposits in both regions minimizes
the variance of
xm and maximizes the benefits of diversification, thus reducing the expected
refinancing cost. (We will come back to this point in Section 5 when studying the effect of
the merger on aggregate liquidity demand.)

Given D1 = D2 , the merged banks choose reserves Rm so as to maximize their combined
profits in (11). Let
km = Dm be the reserve-deposit ratio for the merged banks and recall
that
ksq is the one for banks in the status quo defined in (10). The following proposition
compares these two ratios.

Proposition 2 The merged banks choose a lower reserve-deposit ratio than in the status
quo (
km ksq) if the relative cost of refinancing is higher than a threshold ρ (rrI > ρ), and
a higher one otherwise.

Proposition 2 contains the first main result of the paper indicating that the merged
banks may have a higher or a lower optimal reserve-deposit ratio than individual banks.
The result depends on the relative strength of two effects:

A diversification effect that reduces the probability of extreme shocks for the merged
banks;

An internalization effect consisting in the possibility to use any unit of reserves to
cover a deposit outflow at either of the banks that make up the merged bank. This

15



More intriguing information

1. Macro-regional evaluation of the Structural Funds using the HERMIN modelling framework
2. Automatic Dream Sentiment Analysis
3. The constitution and evolution of the stars
4. The Employment Impact of Differences in Dmand and Production
5. Determinants of U.S. Textile and Apparel Import Trade
6. Testing the Information Matrix Equality with Robust Estimators
7. fMRI Investigation of Cortical and Subcortical Networks in the Learning of Abstract and Effector-Specific Representations of Motor Sequences
8. Input-Output Analysis, Linear Programming and Modified Multipliers
9. The name is absent
10. Graphical Data Representation in Bankruptcy Analysis
11. Qualifying Recital: Lisa Carol Hardaway, flute
12. The name is absent
13. News Not Noise: Socially Aware Information Filtering
14. Monopolistic Pricing in the Banking Industry: a Dynamic Model
15. Distortions in a multi-level co-financing system: the case of the agri-environmental programme of Saxony-Anhalt
16. The name is absent
17. The name is absent
18. Death as a Fateful Moment? The Reflexive Individual and Scottish Funeral Practices
19. Electricity output in Spain: Economic analysis of the activity after liberalization
20. Are class size differences related to pupils’ educational progress and classroom processes? Findings from the Institute of Education Class Size Study of children aged 5-7 Years