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|Title: ||Applying stochastic programming models in financial risk management|
|Authors: ||Yang, Xi|
|Supervisor(s): ||Gondzio, Jacek|
|Issue Date: ||2010|
|Publisher: ||The University of Edinburgh|
|Abstract: ||This research studies two modelling techniques that help seek optimal strategies in
financial risk management. Both are based on the stochastic programming methodology.
The first technique is concerned with market risk management in portfolio
selection problems; the second technique contributes to operational risk management
by optimally allocating workforce from a managerial perspective.
The first model involves multiperiod decisions (portfolio rebalancing) for an asset
and liability management problem and deals with the usual uncertainty of investment
returns and future liabilities. Therefore it is well-suited to a stochastic programming approach.
A stochastic dominance concept is applied to control the risk of underfunding.
A small numerical example and a backtest are provided to demonstrate advantages of
this new model which includes stochastic dominance constraints over the basic model.
Adding stochastic dominance constraints comes with a price: it complicates the
structure of the underlying stochastic program. Indeed, new constraints create a link
between variables associated with different scenarios of the same time stage. This
destroys the usual tree-structure of the constraint matrix in the stochastic program
and prevents the application of standard stochastic programming approaches such as
(nested) Benders decomposition and progressive hedging. A structure-exploiting interior
point method is applied to this problem. Computational results on medium scale
problems with sizes reaching about one million variables demonstrate the efficiency of
the specialised solution technique.
The second model deals with operational risk from human origin. Unlike market
risk that can be handled in a financial manner (e.g. insurances, savings, derivatives),
the treatment of operational risks calls for a “managerial approach”. Consequently,
we propose a new way of dealing with operational risk, which relies on the well known
Aggregate Planning Model. To illustrate this idea, we have adapted this model to the
case of a back office of a bank specialising in the trading of derivative products. Our
contribution corresponds to several improvements applied to stochastic programming
modelling. First, the basic model is transformed into a multistage stochastic program
in order to take into account the randomness associated with the volume of transaction
demand and with the capacity of work provided by qualified and non-qualified
employees over the planning horizon. Second, as advocated by Basel II, we calculate
the probability distribution based on a Bayesian Network to circumvent the difficulty
of obtaining data which characterises uncertainty in operations. Third, we go a step
further by relaxing the traditional assumption in stochastic programming that imposes
a strict independence between the decision variables and the random elements. Comparative
results show that in general these improved stochastic programming models
tend to allocate more human expertise in order to hedge operational risks. The dual
solutions of the stochastic programs are exploited to detect periods and nodes that are
at risk in terms of expertise availability.|
|Keywords: ||risk management|
|Appears in Collections:||Mathematics thesis and dissertation collection|
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