Das Institut für Mathematische Wirtschaftsforschung veranstaltet im Rahmen des Bielefeld Stochastic Afternoon regelmäßig Seminare zum Thema Finanzmathematik. Das Programm des aktuellen Semesters finden Sie hier.
Jean- Paul Décamps (University of Toulouse)
Titel: Integrating profitability prospects and cash management
Abstract: We develop a dynamic corporate finance model in which shareholders learn about the firm's long term profitability and weigh the costs and benefits of holding cash. This leads us to study a new two-dimensional bayesian adaptive control problem that we solve explicitly. We characterize optimal dividend and issuance strategies. The model predicts that the cash target levels are non monotonic in the profitability prospects. This yields novel insights into the relationship between profitability prospects, precautionary cash savings, dividend policy, issuance policy and the dynamics of firm value.
Tolulupe Fadima (University of Freiburg)
Titel: Affine processes under parameter uncertainty
Abstract: We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call \emph{non-linear affine processes}. This is done as follows: given a set $\Theta$ of parameters for the process, we construct a corresponding non-linear expectation on the path space of continuous processes. By a general dynamic programming principle we link this non-linear expectation to a variational form of the Kolmogorov equation, where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters in $\Theta$. This non-linear affine process yields a tractable model for Knightian uncertainty, especially for modelling interest rates under ambiguity. We then develop an appropriate It\^o-formula, the respective term-structure equations and study the non-linear versions of the Vasi\v cek and the Cox-Ingersoll-Ross (CIR) model. Thereafter we introduce the non-linear Vasi\v cek-CIR model. This model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence the approach solves this modelling issue arising with negative interest rates. This is a joint work with Ariel Neufeld and Thorsten Schmidt.
Todor Bilarev (Humboldt-Universität zu Berlin)
Titel: Hedging with transient price impact
Abstract: We solve the superhedging problem for European options in a market with finite liquidity where trading has transient impact on prices, and possibly a permanent one in addition. Impact is multiplicative to ensure positive asset prices. Hedges and option prices depend on the physical and cash delivery specifications of the option settlement. For non-covered options, where impact at the inception and maturity dates matters, we characterize the superhedging price as a viscosity solution of a degenerate semilinear pde that can have gradient constraints. The non-linearity of the pde is governed by the transient nature of impact through a resilience function. For covered options, the pricing pde involves gamma constraints but is not affected by transience of impact. We use stochastic target techniques and geometric dynamic programming in reduced coordinates.
Salvatore Federico (University of Siena)
Titel: Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula
Abstract: Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal control problems. The method applies in the case of additively controlled Ornstein-Uhlenbeck processes, when the associated Hamilton-Jacobi-Bellman (HJB) equation admits a mild solution. The main methodological novelty of our result relies on the fact that it is not needed to prove, as in previous literature, that the mild solution is a strong solution, i.e. a suitable limit of classical solutions of the HJB equation. To achieve our goal we prove a new type of Dynkin formula, which is the key tool for the proof of our main result. This is based on a joint work with Fausto Gozzi.
Damir Filipovic (EPFL and Swiss Finance Institute)
Titel: A Machine Learning Approach to Portfolio Risk Management
Abstract: We develop a general framework for dynamic portfolio risk management in discrete time. We learn the replicating martingale of an insurance asset-liability portfolio from a finite sample using machine learning techniques. The learned replicating martingale outperforms nested Monte Carlo based portfolio risk estimates in the context of a limited computing budget. This is joint work with Lucio Fernandez-Arjona.
David Proemel (University of Oxford)
Titel: Pathwise pricing-hedging duality in continuous time
Abstract: In the analysis of the financial crises 2008, risk caused by financial modelling was identified as one of the main challenges. In order to reduce the model risk, we discuss an economically justified and model-independent approach to finance, which allows us to characterize the typical behaviour of price paths. In this model-independent framework we recover a fundamental result from classical mathematical finance: the pricing-hedging duality. Our robust duality states that, for any financial option, the pathwise super-hedging price of the option coincides with the robust version of the model-price given by the supremum of the expectation of the option with respect to martingale measures.