# Oberseminar Finanz- und Versicherungsmathematik LMU and TUM (WS 2015/2016)

## Organisatoren

Prof. F. Biagini, Prof. C. Czado, Prof. K. Glau, Prof. C. Klüppelberg, Prof. T. Meyer-Brandis, Prof. M. Scherer, Prof. G. Svindland, Prof. R. Zagst

## Termine

**Donnerstag, 1. Oktober 2015**- Vortrag: Beginn 16 Uhr

**Dienstag, 8. Dezember 2015**- 1. Vortrag: 14:15 bis 15:00 Uhr
- 2. Vortrag: 15:00 bis 15:45 Uhr
- Pause: 15:45 bis 16:15 Uhr
- 3. Vortrag: 16:15 bis 17:00 Uhr

**Montag, 18. Januar 2016**- 1. Vortrag: 14:15 bis 15:00 Uhr
- 2. Vortrag: 15:00 bis 15:45 Uhr
- Pause: 15:45 bis 16:15 Uhr
- 3. Vortrag: 16:15 bis 17:00 Uhr
- 4. Vortrag: 17:00 bis 17:45 Uhr

## Programm

#### 01. Dezember 2015:

- Johannes Muhle-Karbe - Hedging with small uncertainty aversion

#### 08. Dezember 2015:

- Erwan Koch (ETH Zürich) - Spatial risk measures and applications to max-stable processes
- Josef Teichmann (ETH Zürich) - On surprising relations between Americans and Europeans
- Bruno Versaevel (EM Lyon) - On the timing of innovation and imitation in dynamic duopoly

#### 18. Januar 2016:

- Griselda Deelstra (Université Libre de Bruxelles) - The Role of the Dependence between Mortality and Interest Rates when pricing Guaranteed Annuity Options
- Olivier Le Courtois (EM Lyon) - q-Credibility
- Daniël Linders (KU Leuven) - Can implied correlation mislead you?
- Jean Jacod (UPMC-Paris 6) - Incomplete financial models: range of option prices and completion through option prices

## Vortragsthemen (soweit bereits feststehend)

### Hedging with small uncertainty aversion

#### Johannes Muhle-Karbe, 01.10.2015 um 16.00 Uhr

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security’s cash gamma. (Joint work with Sebastian Herrmann and Frank Seifried)

### Spatial risk measures and applications to max-stable processes

#### Erwan Koch, 08.12.2015 um 14.15 Uhr

Spatial risk measures and applications to max-stable processes Abstrakt: The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environmental events in the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms for these spatial risk measures. These axioms quantify the sensitivity of the risk measure with respect to the space and are especially linked to spatial diversification. In order to model the loss underlying our definition of spatial risk measure, we apply a damage function to the environmental variable considered. The latter is assumed to follow a max-stable process, very well suited for the modeling of extreme spatial events. Two damage functions are considered, respectively adapted to temperatures and wind speeds. The theoretical properties of the resulting examples of spatial risk measures are studied and some interpretations in terms of insurance are provided.

### On surprising relations between Americans and Europeans

#### Prof. Teichmann, 08.12.2015 um 15.00 Uhr

Following work of Jourdain-Martini we shed some light on a surprising relationship between American and European options motivated by questions from Finance, Analysis and Numerics.

### On the timing of innovation and imitation in dynamic duopoly

#### Herrn Versaevl, 08.12.2015 um 16.15 Uhr

When fixed costs of innovation and imitation differ, strategic competition between duopolists involves either preemption or attrition, the latter being likelier with high uncertainty. We show that industry value is maximized when firms neither delay nor hasten entry, whereas social welfare has local optima in both the attrition and preemption ranges. The social optimum implies a positive imitation cost, and with static business-stealing and sufficient discounting it involves preemption. Finally we endogenize entry barriers and discuss contracting, showing that firms are more likely to rely on secrecy and patents at low imitation costs and that simple licensing schemes are welfare improving.

### The Role of the Dependence between Mortality and Interest Rates when pricing Guaranteed Annuity Options

#### Griselda Deelstra , 18.01.2016 um 14:15 Uhr

In this paper we investigate the consequences on the pricing of insurance contin- gent claims when we relax the typical independence assumption made in the actuarial literature between mortality risk and interest rate risk. Starting from the Gaussian approach of Jalen and Mamon (2009), we consider more general affine models where the mortality and interest rates remain positive and we derive pricing formulas for insurance contracts like Guaranteed Annuity Options (GAOs). In a Wishart affine model, which allows for a non-trivial dependence between the mortality and the in- terest rates, we go far beyond the results found in the Gaussian case by Liu et al. (2014), where the value of these insurance contracts can be explained only in terms of the initial pairwise linear correlation.

### q-Credibility

#### Olivier le Courtois, 18.01.2016 um 15 Uhr

This article extends credibility theory by making a quadratic adjustment that takes into account the squared values of past observations. This approach amounts to introducing non-linearities in the framework, or to considering higher order mo- ments in the computations. We first describe the full parametric approach and, for illustration, we examine the Poisson-gamma and Poisson-single Pareto cases. Then, we look at the non-parametric approach where premiums must be estimated based on data only, without postulating any type of distribution. Finally, we ex- amine the semi-parametric approach where the conditional distribution is Poisson but the unconditional distribution is unknown.

### Can implied correlation mislead you?

#### Daniël Linders, 18.01.2016 um 16:15 Uhr

The implied correlation of a basket of stocks is backed out from option data on the basket and its components and thus reveals information about the dependence under the risk-neutral measure ℚ. However, in many applications (e.g. portfolio selection), the quantity under consideration is the diversification under the real-world measure ℙ. In general, the theoretical risk-neutral probabilities differ from the actual real-world probabilities and dependence structures between random variables will not transfer from the risk-neutral world to the real world. As a result one has to be careful when using popular measures such as the implied correlation to learn about the real-world dynamics of a set of dependent stocks. We consider a financial market with two stocks and show that dependence in the real world can deviate substantially from the implied dependence, without introducing any arbitrage. We show how this gap between implied and realized dependence can be exploited through a trading strategy involving single and multi-asset variance swaps.

### Incomplete financial models: range of option prices and completion through option prices

#### Jean Jacod, 18.01.2016 um 17 Uhr

Except for the Black-Scholes model, financial models are typically incomplete: claims cannot usually be hedged, and there are infinitely many equivalent martingale measures, implying that options don’t have a unique price. We will discuss the possible range for the price of an European option, and show that in some cases it is possible to complete the model by adding to the stock price the price of a traded option. This is a preliminary work and we will essentially state some fairly general facts and examine a few concrete models for which a solution to the previous questions can be attained.