Sascha Desmettre

Worst-Case Consumption-Portfolio Optimization

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash. In an infinite-horizon setting, we provide an explicit solution for constant relative risk aversion and establish a rigorous verification result. Moreover, we find a dual characterization of the optimal strategy and quantify the impact of the crash on consumption and portfolio choice.

Robust worst-case optimal investment

Based on a robustness concept adapted from mathematical statistics, we investigate robust optimal investment strategies for worst-case crash scenarios when the maximum crash height is not known a priori. We specify an efficiency criterion in terms of the certainty equivalents of optimal terminal wealth and explicitly solve the investor’s portfolio problem for CRRA risk preferences. We also study the behavior of the minimax crash height and the efficiency of the associated strategies in the limiting case of infinitely many crashes.

Own-Company Stockholding and Work Effort Preferences of an Unconstrained Executive

We develop a framework for analyzing an executive’s own-company stockholding and work effort preferences. The executive, characterized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive’s utility-maximizing personal investment and work effort strategy is derived in closed form, and a utility indifference rationale is applied to determine his required compensation. Being unconstrained by performance contracting, the executive’s work effort strategy establishes a base case for theoretical or empirical assessment of the benefits or otherwise of constraining executives with performance contracting.

10 Computational Challenges in Finance

With the growing use of both highly developed mathematical models and complicated derivative products at financial markets, the demand for high computational power and its efficient use via fast algorithms and sophisticated hard- and software concepts became a hot topic in mathematics and computer science. The combination of the necessity to use numerical methods such as Monte Carlo simulation, of the demand for a high accuracy of the resulting prices and risk measures, of online availability of prices, and the need for repeatedly performing those calculations for different input parameters as a kind of sensitivity analysis emphasizes this even more. In this survey, we describe the mathematical background of some of the most challenging computational tasks in financial mathematics. Among the examples are the pricing of exotic options by Monte Carlo methods, the calibration problem to obtain the input parameters for financial market models, and various risk management and measurement tasks.

Lifetime Consumption And Investment For Worst-Case Crash Scenarios

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash on an infinite time horizon. We provide a closed-form solution for constant relative risk aversion and establish a rigorous verification result. More specifically, using martingale arguments we demonstrate that the optimal consumption-portfolio strategy can be characterized as the indifference strategy that achieves the best performance in the no-crash scenario. In addition, we find a dual characterization of the optimal strategy as the indifference strategy that minimizes the crash exposure. Finally, we quantify the impact of the crash on consumption and portfolio choice and analyze it in terms of the investors risk and time preferences and prudence.

Estimating discrete dividends by no-arbitrage

We develop and showcase a simple no-arbitrage methodology for the valuation of discrete dividend payments, based exclusively on market prices of options via the put-call parity. Our approach integrates all available option market data and simultaneously calibrates the market-implied discount curve, thus ensuring consistency across spot and derivative markets. We illustrate our method using stocks of European blue-chip companies.

Modeling Redemption Risks of Mutual Funds Using Extreme Value Theory

We show how redemption risks of mutual funds can be modeled using the peaks-over-threshold approach from extreme value theory. The resulting risk measure liquidity-at-risk is adapted to cover issues arising when fund redemption data from the real world is used, and we give guidelines for what should be considered in practice. We also provide an automated and easily applicable procedure for determining the threshold parameter of a generalized Pareto distribution by means of a given data set. Moreover, we supplement our findings with a thorough backtesting analysis.

Optimization strategies for portable code for Monte Carlo-based value-at-risk systems

Value-at-risk (VaR) computations are one important basic element of risk analysis and management applications. On the one hand, risk management systems need to be flexible and maintainable, but on the other hand they require a very high computational power. In general, accelerators provide high speedups, but come with a limited flexibility. In this work, we investigate two approaches towards portable and fast code for VaR computations on heterogeneous platforms: operator tuning and the use of OpenCL. We show that operator tuning can save up one third of run time on CPU-based systems in the calibration step. For OpenCL, we present a detailed analysis of run time on CPU, GPU, and Xeon Phi, and evaluate its portability. We also find that the same code runs up to 12x faster in a VaR setting with an accelerator card being present, without any code changes required.

Work Effort, Consumption, and Portfolio Selection: When the Occupational Choice Matters

We consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market including the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility. The power utility case is discussed as well. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two positions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibility to benefit from her work effort by acquiring own-company shares. This gives insight into aspects of optimal contract design. Our framework is applicable to the pharmaceutical and financial industry, and the IT sector.

Generalized Pareto processes and fund liquidity risk

Motivated by the modelling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP and a thresholded ARGP. These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which is to be estimated in advance). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.