PRisMa 2011

Prof. Dr. Uwe Schmock
(FAM @ TU Wien)
Welcome

Dr. Stefan Gerhold
(FAM @ TU Wien)

Transaction Costs, Trading Volume, and the Liquidity Premium
Abstract: In a market with one safe and one risky asset, an investor with a long horizon and constant relative risk aversion trades with constant investment opportunities and proportional transaction costs. We derive the optimal investment policy, its welfare, and the resulting trading volume, explicitly as functions of the market and preference parameters, and of the implied liquidity premium, which is identified as the solution of a scalar equation. For small transaction costs, all these quantities admit asymptotic expansions of arbitrary order. The results exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also derived explicitly. (Joint work with Paolo Guasoni, Johannes Muhle-Karbe, and Walter Schachermayer.)

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Coffee Break

Chairperson: Prof. Dr. Friedrich Hubalek

Dr. Beatrice Acciaio
(University of Perugia and Vienna University)

On the Lower Arbitrage Bound of American Contingent Claims
Abstract: We prove that in a discrete-time market model the lower arbitrage bound of an American contingent claim is itself an arbitrage-free price if and only if it corresponds to the price of the claim optimally exercised under some equivalent martingale measure.

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Dipl.-Math. Tilmann Blümmel
(FAM @ TU Wien)

Brownian Moving Averages and Applications Towards Interest Rate Modelling
Abstract: Classical interest rate models driven by Brownian motion differ from observed interest rates for several reasons; in particular these models lack to simulate "long memory" properties of the increments, which can be observed in financial data [cf. Cont (1997)] and exhibit a different scaling behaviour. Several authors propagate scaling according to a power law, which is realized by fractional Brownian motion. First investigations of financial data provided by Bank Austria showed, that the scaling behaviour of interest rates is even more complex. Moreover it is well known that fractional Brownian motion is not a semimartingale therefore it allows for arbitrage [cf. Cheridito (2001), Rogers (1997)]. We present a flexible class of Brownian moving averages (BMA) in continuous time, studied by Cherny (2001), Basse (2008), and others, that are semimartingales, and thus ensure the absence of arbitrage and exihibt a wide range of different scaling behaviours. We also sketch our work in progress, a Vasicek-type interest rate model driven by a BMA-semimartingale. (Joint work with Friedrich Hubalek.)

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Lunch Break

Chairperson: Prof. Dr. Peter Grandits

Dr. Julia Eisenberg
(FAM @ TU Wien)

Optimal Control of Capital Injections by Reinsurance With and Without Regime Switching
Abstract: We consider an insurance company, where the claims are reinsured by some reinsurance. Concerning the surplus of the insurance company two different cases are studied. In the first case the surplus process is supposed to follow a diffusion; in the second case we let the drift and the volatility of the diffusion-surplus depend on an observable continuous-time Markov chain. This Markov chain represents regime switching - the macroeconomic changes impacting the parameters of our model. Our objective is to minimize the value of expected discounted capital injections, which are necessary to keep the risk process above zero. Thus, we goal to find the value function defined as the infimum of expected discounted capital injections over all reinsurance strategies; and to derive the optimal strategy leading to the value function. Whereas in the case of a "simple" diffusion the value function is an exponential function, things are different in the case of regime switching. A general form explicit solution could not be given. However, we illustrate how the value function can be calculated by a simple example with a two states Markov chain.

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Dr. Gregory Temnov
(University College Cork)

Problem of Random Summation and Its Role in Risk Aggregation Models
Abstract: Risk aggregation is one of the key points in most of risk models. In order to provide a reliable estimation of aggregated risk, a suitable methodology should be chosen and efficient numerical techniques should be developed. Basing on the series of our recent publications, we make a general overview of basic problems of risk aggregation, along with some specific aspects relevant for practical applications. Our investigation includes theoretical analysis of the influence of general economic factors, such as inflation and general economic trends, on risk estimation, as well as practical studies employing numerical techniques such as Bayesian inference and Quasi-Monte Carlo method in the framework of risk aggregation.

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Coffee Break

Chairperson: Prof. Dr. Uwe Schmock

Jonas Hirz, MSc
(FAM @ TU Wien)

Design of Optimal Cost-Efficient Payoffs and Corresponding Investment Contracts
Abstract: Bernard and Boyle (2010), as well as Bernard, Maj and Vanduffel (2010) employed the preference-free framework introduced by Dybvig (1988) and Cox and Leland (1982, 2000) to optimize the structure of dynamic investment strategies. They give a characterization of the payoff with the lowest cost among the set of all payoffs with the same distribution at maturity. We drop the assumption of continuity of the state-price density at maturity in order to get some modest generalizations to previous results. We introduce "expanded", optimal real-valued random variables built upon the concepts of comonotonicity and countermonotonicity. Our more general results cover discrete cases, as in Dybvig (1988), as well as continuous cases, as in Bernard and Boyle (2010). Furthermore, we see the important influence of cost-efficiency on the behaviour of profit-seeking investors in a fairly general preference framework and its connection to first-order stochastic dominance. Subsequently, we analyse the optimization of payoffs under the preference framework of risk-averse investors and its relationship to second-order stochastic dominance. Then we take a closer look at a call option in a one-dimensional Black-Scholes market with deterministic time-dependent coefficients. There we point out a significant difference to the case of constant coefficients, as done in Bernard and Boyle (2010). Finally, we introduce a simple stochastic drift which induces a jump in the state-price density at maturity in this special Black-Scholes market in order to justify our extensions. (Joint work with Uwe Schmock.)

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Dipl.-Ing. Karin Hirhager
(FAM @ TU Wien)

Adapted Dependence
Abstract: We consider claims which have a pay-out determined by a stochastic process and a stopping time or an adapted random probability measure. Our main assumption is that we allow these to be dependent and that the stopping time, or the adapted random probability measure respectively, follows a predefined distribution. We present the setting used for this problem as well as upper and lower bounds. For some special cases we also present exact solutions. Further we show some applications for the introduced problem. (Joint work with Uwe Schmock.)

Bread and Wine