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- Black-Scholes model (1)
- CWGAN (1)
- Capital-at-Risk (1)
- Electricity consumption (1)
- Generative adversarial networks (1)
- Impulse control (1)
- Optimal portfolios (1)
- RCGAN (1)
- RCWGAN (1)
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Load modeling is one of the crucial tasks for improving smart grids’ energy efficiency. Among many alternatives, machine learning-based load models have become popular in applications and have shown outstanding performance in recent years. The performance of these models highly relies on data quality and quantity available for training. However, gathering a sufficient amount of high-quality data is time-consuming and extremely expensive. In the last decade, Generative Adversarial Networks (GANs) have demonstrated their potential to solve the data shortage problem by generating synthetic data by learning from recorded/empirical data. Educated synthetic datasets can reduce prediction error of electricity consumption when combined with empirical data. Further, they can be used to enhance risk management calculations. Therefore, we propose RCGAN, TimeGAN, CWGAN, and RCWGAN which take individual electricity consumption data as input to provide synthetic data in this study. Our work focuses on one dimensional times series, and numerical experiments on an empirical dataset show that GANs are indeed able to generate synthetic data with realistic appearance.
We consider the optimization problem of a large insurance company that wants to maximize the expected utility of its surplus through the optimal control of the proportional reinsurance. In addition, the insurer is exposed to the risk of default of its reinsurer at the worst possible time, a setting that is closely related to a scenario of the Swiss Solvency Test.
As a consequence of the real estate market crash after 2008, large investors invested a significant amount of wealth into single-family houses to construct a portfolio of rental dwellings, whose income is securitized in the capital. In some local housing markets, these investors own remarkable numbers of single-family houses. Furthermore, their trading activities have resulted in a new investment strategy, which exacerbates property wealth concentration and polarization. This new investment strategy and its portfolio optimization inspire curiosity about its influence on housing markets. This paper first aims to find an optimal portfolio strategy by employing an expected utility optimization from the terminal wealth, which adopts a stochastic model that includes a variety of economic states to estimate house prices. Second, it aims to analyze the effect of large investors on the housing market. The results show the investment strategies of large investors depend on the balance among economic state, maintenance cost, rental income, interest rate and investment willingness of large investors to housing and their effect depends on the state of the economy.
Die Möglichkeit einer Prämienanpassung in der deutschen PKV ist vom Wert des sogenannten auslösenden Faktors abhängig, der mittels einer linearen Extrapolation der Schadenquotienten der vergangenen drei Jahre berechnet wird. Seine frühzeitige, verlässliche Vorhersage ist aus Sicht des Risikomanagements von großer Bedeutung. Wir untersuchen deshalb vielfältige Vorhersageansätze, die von klassischen Zeitreihenansätzen und Regression über neuronale Netze bis hin zu hybriden Modellen reichen. Während bei den klassischen Methoden Regression mit ARIMA-Fehlern am besten abschneidet, zeigt ein neuronales Netz, das mit Zeitreihenvorhersage kombiniert oder auf desaisonalisierten und trendbereinigten Daten trainiert wurde, das insgesamt beste Verhalten.
Various regulatory initiatives (such as the pan-European PRIIP-regulation or the German chance-risk classification for state subsidized pension products) have been introduced that require product providers to assess and disclose the risk-return profile of their issued products by means of a key information document. We will in this context outline a concept for a (forward-looking) simulation-based approach and highlight its application and advantages. For reasons of comparison, we further illustrate the performance of approximation methods based on a projection of observed returns into the future such as the Cornish–Fisher expansion or bootstrap methods.
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.
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.
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.
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.
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.