Stochastic Analysis and Stochastic Finance Seminar

Model risk of contingent claims

Speaker(s): 
Natalie Packham (Hochschule für Wirtschaft und Recht Berlin)
Date: 
Thursday, October 20, 2016 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models.

Additional information and pricing-hedging duality in robust framework

Speaker(s): 
Anna Aksamit (University of Oxford)
Date: 
Thursday, July 7, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In robust approach, instead of choosing one model, one considers superhedging simultaneously under a family of models, or pathwise on the set of feasible trajectories. Usually in the literature the focus is on the natural filtration $\mathbb F$ of the price process. Here we extend that to a general filtration $\mathbb G$ including the natural filtration of the price process $\mathbb F\subset \mathbb G$. Two filtrations can model asymmetry of information on the market.

Stochastic Control Methods for Optimal Government Debt Management

Speaker(s): 
Abel Cadenillas (University of Alberta)
Date: 
Thursday, June 23, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

Motivated by the debt crisis in the world, we apply methods of stochastic control to study two problems related to government debt management. In the first problem, we consider a government that wants to control its debt ratio. The debt generates a cost for the country. The government can reduce its debt ratio, but there is a cost associated with this reduction. We apply the theory of stochastic singular control to obtain an explicit formula for the optimal government debt ceiling.

Continuous-state Branching Processes in Random Environment

Speaker(s): 
Wei Xu (Beijing Normal University)
Date: 
Thursday, June 23, 2016 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

Motivated by the study of negative jumps in finance/biology, we introduce a general continuous-state branching process in random environment (CBRE-process) defined as the strong solution of a stochastic integral equation. The environment is determined by a Levy process with jumps no less than $-1$. We give characterizations of the quenched and annealed transition semigroups of the process in terms of a backward stochastic integral equation driven by another Levy process determined by the environment.

Stochastic control for a class of nonlinear kernels and applications

Speaker(s): 
Chao Zhou (National University of Singapore)
Date: 
Thursday, June 9, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

A stochastic control problem for a class of nonlinear stochastic kernels is studied. We prove a dynamic programming principle (DPP) for the value function by a measurable selection argument and consider several applications of the DPP including the wellposedness of second order BSDEs.
This is a joint work with Dylan POSSAMAI and Xiaolu TAN.

Optimal investment in markets with friction

Speaker(s): 
Miklos Rasonyi (Renyi Institute, Budapest)
Date: 
Thursday, June 9, 2016 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We will treat optimal investment in a continuous-time market with instantaneous price impact. The novelty lies in going beyond concave utility functions and allowing non-concave preferences as well as probability distortions in the agent's objective function. This allows to treat e.g. cumulative prospect theory preferences. The main technical tool is an extension of Skorohod's representation theorem for weakly convergent sequences of probabilities.

Super-replication in extremely incomplete markets

Speaker(s): 
Yan Dolinsky (The Hebrew University of Jerusalem)
Date: 
Thursday, May 26, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In this work we introduce the notion of extremely incomplete markets. We prove that for these markets the super–replication price coincide with the model free super–replication price. Namely, the knowledge of the model does not reduce the super–replication price. We provide two families of extremely incomplete models: stochastic volatility models and rough volatility models. Moreover, we give several computational examples. Our approach is purely probabilistic. (joint work with A.Neufeld)

Uncertainty and Robustness in Stochastic Filtering

Speaker(s): 
Samuel Cohen (University of Oxford)
Date: 
Thursday, May 26, 2016 - 4:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

In this talk we shall consider a rigorous and systematic approach to uncertainty in problems of filtering in discrete time, using the structure of nonlinear expectations and risk measures. We shall show that, under general conditions relating the perception of uncertainty and the observation filtration, one has a forward recursion which describes the uncertainty over the current state of an unobserved process. In the setting of a discrete-time hidden Markov chain, or of the Kalman filter, we shall also obtain simple approximations which can be implemented in real time.

Probabilistic Representation for Viscosity Solution of Fully nonlinear Stochastic PDEs

Speaker(s): 
Anis Matoussi (Universite du Maine, Le Mans)
Date: 
Thursday, May 12, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the generator, and we investigate the links between the 2BDSDEs and a class of parabolic fully nonlinear Stochastic PDEs. Precisely, we show that the Markovian solution of 2BDSDEs provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear SPDEs. This presentation includes some applications in pathwise stochastic control problems.

Asymptotic Lower Bounds for Optimal Tracking a Linear Programming Approach

Speaker(s): 
Mathieu Rosenbaum (Université Pierre et Marie Curie, Paris 6)
Date: 
Thursday, April 28, 2016 - 5:00pm
Location: 
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control problem of Brownian motion, which is characterized as a deterministic linear programming. A comprehensive list of examples with explicit expressions for the lower bounds is also provided. This is joint work with Jiatu Cai and Peter Tankov.

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