# Finance and Insurance Seminar WS 2010/11

**14. Oktober**:

**Hanqing Jin, University of Oxford**

**“Behavioural Portfolio Selection - Loss aversion and Bounded Loss”**

**Abstract:**

Behavioural finance is a developing theory for modeling people's decision in the real world, which can deviate from the rational optimality in the classical decision theory. This talk will start from the latest portfolio selection model for investors with behavioural objective. And then I will introduce how to solve the optimal portfolio, which turns out to be lower bounded automatically because of the loss aversion of the investor. Unfortunately, the possible loss of the optimal portfolio may still be unacceptably huge. In the last part of this talk, we impose an exogenous constraint on the loss and study the problem with bounded loss.

**28. Oktober**:

**Andreas Pfingsten, University of Münster**

**"Bank Lines of Credit in Liquidity Management - The Impact of Recall Risk for German SMEs"**

(joint work with Carsten Hubensack (Finance

Center Münster) and Andrea Schertler (University

of Groningen)

**Abstract:**

We use a unique sample of bank lines of credit (hereafter: lines) provided by a German universal bank to investigate how SMEs (small and medium-sized enterprises) use such lines in their liquidity management. The bank does not require an upfront fee for providing a line but the interest rate for using it is higher than those on alternative regular loans. Thus, using the line as a permanent funding tool is inefficient for SMEs, but the line can substitute costly cash holdings since it provides liquidity on demand. Since the bank has the right to recall the lines upon short notice, a major difference when compared with the lines underlying previous studies, we analyze how this recall risk impacts on the SME's cash holdings and line usage. As expected on the basis of theoretical considerations, we find the following non-linear and, for the first time, non-monotonic coherence: SMEs facing low recall risks have lower cash holdings and higher line usage than SMEs facing moderate recall risk because the latter hold further cash to insure against losing the line. In turn, SMEs facing moderate recall risk have higher cash holdings and lower line usage than SMEs facing high recall risk because the latter are most likely in a worse financial situation, which makes cash holding too expensive. Moreover, we find that SMEs with a line hold less cash than those without a line.

**11.November**

**Rüdiger Frey, University of Leipzig**

**"Optimal Securitization of Credit Portfolios via Impulse Control"**

Abstract:

Abstract:

We study the optimal loan securitization policy of a commercial bank which is mainly engaged in lending activities. For this we propose a stylized dynamic model which contains the main features affecting the securitization decision. In line with reality we assume that there are non-negligible fixed and variable transaction costs associated with each securitization. The fixed transaction costs lead to a formulation of the optimization problem in an impulse control framework. We prove

viscosity solution existence and uniqueness for the quasi-variational inequality associated with this impulse control problem. Iterated optimal stopping is used to find a numerical solution of this PDE, and numerical examples are discussed.

**2.Dezember:**

**Andreas Tsanaka, Cass Business School London**

**"Parameter uncertainty in insurance solvency and pricing**"

**Abstract:**

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decision maker is able to set the threshold at an appropriate level. This general situation applies for example to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls.

However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. It shown that parameter uncertainty increases the probability (understood as expected frequency) of failures.

For a large class of loss distributions, arising from increasing

transformations of location-scale families (including the Log-Normal, Weibull and Pareto distributions), failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (a) by reducing the nominal required failure probability, depending on the size of the available data set and (b) by modifying of the distribution itself that is used to calculate the risk control. Approach (a) corresponds to a frequentist/regulatory view of probability, while approach (b) is consistent with a Bayesian/personalistic view. It then shown that the two approaches are consistent in achieving the required failure probability.

Moving from solvency to a pricing framework, we argue that estimation bias may be the main source of error in pricing a homogenous portfolio. In particular it is shown that for loss distributions in 1-parameter exponential families (such as the popular Pareto curve), the MLE of expected loss cost of high layers will be subject to substantial positive bias. Moreover, the use of predictive loss distributions, which was helfpful in solvency-related applications, only makes the problem of bias worse. A parametric bootstrap approach to bias correction is discussed. The analysis in this part of the talk is based on asymptotic expansions used to evaluate the expected values of functionals of sample means.

**6. Januar:**

**Freddy Delbaen, ETH Zürich**

**"The structure of time consistent utility functions"**

(joint work with S.Peng, E. Rosazza-Gianin, X. Bao and Y. Hu)

(joint work with S.Peng, E. Rosazza-Gianin, X. Bao and Y. Hu)

Abstract:

Abstract:

Monetary utility functions that are consistent in time have a special structure. In the case of a Brownian filtration, we will give a complete answer. The corresponding utility functions

are given by solutions of Backward Stochastic Differential Equations. However these equations do not always have a unique solution. The utility functions is then the biggest of all these solutions.

**13. Januar:**

**Fabio Trojani, University of Lugano**

**27. Januar**

**Holger Kraft, University of Frankfurt**