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Mon, 10 Apr 2000 00:00:00 +0200Mon, 10 Apr 2000 00:00:00 +0200Some Applications of Impulse Control in Mathematical Finance
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1143
We consider three applications of impulse control in financial mathematics, a cash management problem, optimal control of an exchange rate, and portfolio optimisation under transaction costs. We sketch the different ways of solving these problems with the help of quasi-variational inequalities. Further, some viscosity solution results are presented.Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1143Wed, 04 Oct 2000 00:00:00 +0200A stochastic control approach to portfolio problems with stochastic interest rates
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1142
We consider investment problems where an investor can invest in a savings account, stocks and bonds and tries to maximize her utility from terminal wealth. In contrast to the classical Merton problem we assume a stochastic interest rate. To solve the corresponding control problems it is necessary to prove averi cation theorem without the usual Lipschitz assumptions.Ralf Korn; Holger Kraftpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1142Mon, 18 Sep 2000 00:00:00 +0200A martingale method of portfolio optimization for unobservable mean rate of return
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1141
In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.Juri Hinz; Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1141Mon, 11 Sep 2000 00:00:00 +0200On value preserving and growth optimal portfolios
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1133
In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with the minimal martingale measure only for complete markets.Ralf Korn; Manfred Schälpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1133Tue, 29 Aug 2000 00:00:00 +0200Value Preserving Strategies and a General Framework for Local Approaches to Optimal Portfolios
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1120
We present some new general results on the existence and form of value preserving portfolio strategies in a general semimartingale setting. The concept of value preservation will be derived via a mean-variance argument. It will also be embedded into a framework for local approaches to the problem of portfolio optimisation.Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1120Mon, 28 Aug 2000 00:00:00 +0200Optimal portfolios under the threat of a crash
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1122
We consider the determination of optimal portfolios under the threat of a crash. Our main assumption is that upper bounds for both the crash size and the number of crashes occurring before the time horizon are given. We make no probabilistic assumption on the crash size or the crash time distribution. The optimal strategies in the presence of a crash possibility are characterized by a balance problem between insurance against the crash and good performance in the crash-free situation. Explicit solutions for the log-utility case are given. Our main finding is that constant portfolios are no longer optimal ones.Ralf Korn; Paul Wilmottpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1122Mon, 28 Aug 2000 00:00:00 +0200Optimal portfolios with bounded Capital-at-Risk
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1123
We consider some continuous-time Markowitz type portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the Capital-at-Risk. In a Black-Scholes setting we obtain closed form explicit solutions and compare their form and implications to those of the classical continuous-time mean-variance problem. We also consider more general price processes which allow for larger uctuations in the returns.Susanne Emmer; Claudia Klüppelberg; Ralf Kornpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1123Mon, 28 Aug 2000 00:00:00 +0200