Abstracts
Theresa Traxler - Portfolio Insurance under Price Impact: An Optimal Stopping Approach
Portfolio insurance enables investors to limit downside risk through a capital guarantee, while retaining upside potential in rising markets. We extend classical portfolio insurance models by incorporating realistic market frictions, including temporary and permanent price impact, liquidation cost and optimal stopping, providing a more robust foundation for these strategies. The resulting problem models a portfolio manager dynamically trading a risky asset under a capital guarantee at maturity, with the objective of maximizing the expected value at liquidation. We analyze different scenarios: continuous trading with and without penalization, as well as optimal trading and stopping. The case of continuous trading without penalization has a classical solution, while for the other cases we rely on viscosity theory. We also solve all problems numerically using a Newton algorithm.
Luna Rigby - If Not Now, Then When? Model Risk in the Optimal Exercise of American Options
Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper analyzes model risk in the optimal exercise of an American put option using the benchmark methodology of Hull and Suo [2002]. The true data-generating process is assumed to follow a Heston stochastic volatility model. We compare the optimal exercise strategy of an investor who correctly uses the Heston model with those of investors who instead use misspecified Black-Scholes or Dupire local volatility models. Optimal exercise boundaries are computed numerically via finite difference methods. Stochastic volatility dynamics and return-volatility correlation are found to have a substantial impact on optimal exercise behavior across models, creating a source of model risk. As this behavior is not transmitted to exercise strategies determined by misspecified models, even if such models are fully calibrated to European option prices, calibration fails to mitigate model risk in this context. This issue persists under frequent recalibration of a misspecified model.
Mustafa Colak - Dynamic mean-variance problem: recovering time-consistency
As the foundation of modern portfolio theory, Markowitz's mean-variance portfolio optimization problem is one of the fundamental problems of financial mathematics. The dynamic version of this problem in which a positive linear combination of the mean and variance objectives is minimized is known to be time-inconsistent, hence the classical dynamic programming approach is not applicable. Following the dynamic utility approach in the literature, we consider a less restrictive notion of time-consistency, where the weights of the mean and variance are allowed to change over time. Precisely speaking, rather than considering a fixed weight vector throughout the investment period, we consider an adapted weight process. Initially, we start by extending the well-known equivalence between the dynamic mean-variance and the dynamic mean-second moment problems in a general setting. Thereby, we utilize this equivalence to give a complete characterization of a time-consistent weight process, that is, a weight process which recovers the time-consistency of the mean-variance problem according to our definition. We formulate the mean-second moment problem as a biobjective optimization problem and develop a set-valued dynamic programming principle for the biobjective setup. Finally, we retrieve back to the dynamic mean-variance problem under the equivalence results that we establish and propose a backward-forward dynamic programming scheme by the methods of vector optimization. Consequently, we compute both the associated time-consistent weight process and the optimal solutions of the dynamic mean-variance problem.