DGVFM-Minisymposium Schedule_DAV

Prof. Dr. Alexander Szimayer
Chair for Finance (Derivatives)
Universität Hamburg
Fakultät für Wirtschafts- und Sozialwissenschaften
Von-Melle-Park 5
20146 Hamburg
Tel.: +49 40 42838 9119
Email: [email protected]
DGVFM-Minisymposium
in Financial and Insurance Mathematics
Session 1
Wednesday, Sept. 23, 2015
Venue: Hörsaal K, Edmund-Siemers-Allee 1 (Main Building)
Chair: Prof. Dr. Alexander Szimayer (Universität Hamburg)
10:30 – 11:10
Prof. Dr. Jan Kallsen (Christian-Albrechts-Universität zu Kiel)
Are American options European after all?
11:10 – 11:50
Prof. Dr. Stefan Weber (Leibniz Universität Hannover)
Measures of Systemic Risk
11:50 – 12:30
Dr. Sascha Desmettre (Technische Universität Kaiserslautern)
Optimal Investment with Illiquid Assets
Evening: DMV-conference dinner.
Please register at the DMV conference website (not included in registration fee).
Session 2
Thursday, Sept. 24, 2015
Venue: Room 223, Edmund-Siemers-Allee 1 (Main Building)
Chair: Dr. Christian Hilpert (Universität Hamburg)
10:30 – 11:10
Dr. Peter Hieber (Universität Ulm)
Risk-shifting & optimal asset allocation in life insurance: the impact of regulation
11:10 – 11:50
Prof. Dr. Rudi Zagst (Technische Universität München)
Pricing of Variable Annuities - Incorporation of Policyholder Behavior
11:50 – 12:30
Prof. Dr. Christoph Kühn (Goethe-Universität Frankfurt)
Modeling capital gains taxes in continuous time
Session 1
Prof. Dr. Jan Kallsen (Christian-Albrechts-Universität zu Kiel)
Are American options European after all?
Christensen (Mathematical Finance 24, 2014, 156-172) has introduced an efficient numerical approach for obtaining upper bounds of American option prices in diffusion models. It relies on approximating the value of the
option by European options with a larger payoff. In this talk we discuss the question whether or to what extent
the value of an American option actually coincides on the continuation region with that of a properly chosen
European payoff. In analytical terms this boils down to the question whether the harmonic function solving a
free
boundary
problem
can
be
extended
to
a
harmonic
function
on
the
whole
space.
Prof. Dr. Stefan Weber (Leibniz Universität Hannover)
Measures of Systemic Risk
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of
the system itself. The tremendous cost of this type of risk requires the design and implementation of tools for
the efficient macroprudential regulation of financial institutions. We propose a novel approach to measuring
systemic risk.
Key to our construction is a rigorous derivation of systemic risk measures from the structure of the underlying
system and the objectives of a financial regulator. The suggested systemic risk measures express systemic risk
in terms of capital endowments of the financial firms. Their definition requires two ingredients: first, a random
field that assigns to the capital allocations of the entities in the system a relevant stochastic outcome. The second ingredient is an acceptability criterion, i.e. a set of random variables that identifies those outcomes that are
acceptable from the point of view of a regulatory authority. Systemic risk is measured by the set of allocations
of additional capital that lead to acceptable outcomes. The resulting systemic risk measures are set-valued and
can be studied using methods from set-valued convex analysis. At the same time, they can easily be applied to
the regulation of financial institutions in practice.
We explain the conceptual framework and the definition of systemic risk measures, provide an algorithm for
their computation, and illustrate their application in numerical case studies. We apply our methodology to
systemic risk aggregation as described in Chen, Iyengar & Moallemi (2013) and to network models as suggested
in the seminal paper of Eisenberg & Noe (2001), see also Cifuentes, Shin & Ferrucci (2005), Rogers & Veraart
(2013), and Awiszus & Weber (2015). This is joint work with Zachary G. Feinstein and Birgit Rudloff.
Dr. Sascha Desmettre (Technische Universität Kaiserslautern)
Optimal Investment with Illiquid Assets
We study asset allocation decisions of an investor that has the opportunity to invest in an illiquid asset that is
only traded at time 0. We use a generalized martingale approach to find the optimal terminal wealth and to
determine the optimal amount invested in the illiquid asset. We also characterize optimal trading strategies via
Clark’s formula and provide a simple representation in terms of a liquidity-related derivative. As an application,
we study optimal asset allocation with fixed-term deposits and fixed-term defaultable investments. We
demonstrate that the presence of such investment opportunities can have a significant impact on asset allocation: CRRA agents with realistic values of relative risk aversion optimally allocate more than 40% of their
wealth to illiquid assets if these yield a moderate excess return of 100 basis points over the money market account.
2
Session 2
Dr. Peter Hieber (Universität Ulm)
Risk-shifting & optimal asset allocation in life insurance: The impact of regulation
In a typical participating life insurance contract, the insurance company is entitled to a share of the return surplus as compensation for the return guarantee granted to policyholders. This call-option-like stake gives the
insurance company an incentive to increase the riskiness of its investments at the expense of the policyholders.
This conflict of interests can partially be solved by regulation deterring the insurance company from taking
excessive risk. In a utility-based framework where default is modeled continuously by a structural approach,
we show that a flexible design of regulatory supervision can be beneficial for both the policyholder and the
insurance company.
Prof. Dr. Rudi Zagst (Technische Universität München)
Pricing of Variable Annuities - Incorporation of Policyholder Behavior
Variable annuities represent certain unit-linked life insurance products offering different types of protection
commonly referred to as guaranteed minimum benefits (GMXBs). They are designed for the increasing demand
of the customers for private pension provision. We propose a framework for the pricing of variable annuities
with guaranteed minimum repayments at maturity and in case of the insured’s death. If the policyholder
prematurely surrenders this contract, his right of refund is restriced to the current value of the fund account
reduced by the prevailing surrender fee. For the financial market and the mortality model an affine linear setting is chosen. For the surrender model a Cox process is deployed whose intensity is given by a deterministic
function (s-curve) with stochastic inputs of the financial market. Hence, the policyholders’ surrender behavior
depends on the performance of the financial market and is stochastic. The presented pricing framework allows
for an incorporation of the so-called interest-rate, moneyness, and emergency-fund hypothesis and is based on
suitable closed-form approximations.
Prof. Dr. Christoph Kühn (Goethe-Universität Frankfurt)
Modeling capital gains taxes in continuous time
In most countries, trading gains have to be taxed. The modeling is complicated by the rule that gains on assets
are taxed when assets are sold and not when gains actually occur. This means that an investor can influence
the timing of her tax payments, i.e., she holds a timing option. In this talk, it is shown how the tax payment
stream can be constructed beyond trading strategies of finite variation.
In addition, we analyze Constant Proportion Portfolio Insurance (CPPI) strategies in models with capital gains
taxes and an It\^o asset price process. CPPI strategies invest a constant fraction of some cushion in a risky asset
(or index). For a fraction bigger than one, this leads to a superlinear participation in upward price movements
while guaranteeing a given part of the invested capital, even if the cushion gets completely lost. It turns out
that the associated tax payment stream is of finite variation if the fraction is bigger or equal to one and of infinite variation otherwise.
(Parts of the talk are based on joint work with Björn Ulbricht)
3